単項化問題に関する文献 (2012 年 2 月更新版)

[1] D. Hilbert : Die Theorie der algebraischen Zahlkörper (Satz 94 in Zweiter Teil, Capitel XII, §48.), Jahresber. Deutsch. Math.-Verein. IV (1897), 175–546;

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DigiZeitschriften; reprinted in David Hilbert Gesammelte Abhandlungen, Erster Band: Zahlentheorie, J. Springer, Berlin, 1932, 7, S. 63–355; PPN237821559_log23.pdf (32,30 MB), GDZ; reprinted by Chelsea Publshing Company, Bronx, New York, 1965; Zweite Auflage: Springer-Verlag, Berlin and New York, 1970.

[2] Ph. Furtwängler : Über das Verhalten der Ideale des Grundkörper im Klassenkörper, Monatsh. Math. Phys. XXVII (1916), no. 1, 1–15; DOI: 10.1007/BF01726735 [u620v4x1j2w55671.pdf (613.4 KB)]; [gif], alo; MR1548760; JFM 46.0246.01 (reviewed by Hecke) [html, DVI, ps, PDF, TeX].

[3] E. Artin : Beweis des allgemeinen Reziprozitätsgesetzes, Abh. Math. Sem. Univ. Hamburg 5 (1927), 353–363; DOI: 10.1007/BF02952531 [j08p54lk80w37602.pdf (595.9 KB)]; reprinted in The Collected Papers of Emil Artin (S. Lang and J. Tate, eds.), Addson-Wesley Publ. Co., Inc. Reading, Mass.-London, 1965, CLASS FIELD THEORY, 5, pp. 131–141; reprinted by Springer-Verlag, New York and Berlin, 1982; JFM 53.0144.04 (reviewed by H. Hasse) [html, DVI, ps, PDF, TeX].

[4] Ph. Furtwängler : Beweis des Hauptidealsatzes für Klassenkörper algebraischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 7 (1929), 14–36; DOI: 10.1007/BF02941157 [022633652849278v.pdf (1006.9 KB)]; JFM 55.0699.02 (reviewed by A. Scholz und O. Taussky) [html, DVI, ps, PDF, TeX].

[5] E. Artin : Idealklassen in Oberkörpern und allgemeine Reziprozitätsgesetz, Abh. Math. Sem. Univ. Hamburg 7 (1929), 46–51; DOI: 10.1007/BF02941159 [177h1251672l8778.pdf (353.2 KB)]; reprinted in The Collected Papers of Emil Artin (S. Lang and J. Tate, eds.), Addson-Wesley Publ. Co., Inc. Reading, Mass.-London, 1965, CLASS FIELD THEORY, 7, pp. 159–164; reprinted by Springer-Verlag, New York and Berlin, 1982; JFM 55.0699.01 (reviewed by A. Scholz) [html, DVI, ps, PDF, TeX].

[6] S. Iyanaga : Über der allgemeinen Hauptidealsatz, Japan. J. Math. [日本數學集報] 7 (1930), 315–333; 7_315.pdf (1615 K), Journal@rchive, JST; reprinted in Shokichi Iyanaga Collected Papers, Iwanami Shoten Publishers, Tokyo, 1994, pp. 15–33; Zbl 0002.12101 (reviewed by Taussky) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 57.0207.01 (reviewed by F. Neiß) [html, DVI, ps, PDF, TeX].

[7] H. Hasse : Zum Hauptidealsatz der komplexen Multiplikation, Monatsh. Math. Phys. XXXVIII (1931), no. 1, 315–322; DOI: 10.1007/BF01700702 [n74k8381281j8987.pdf (288.8 KB)]; reprinted in Helmut Hasse Mathematische Abhandlungen, Band 2, de Gruyter, Berlin, 1975, VI. Komplexe Multiplikation, 35, S. 53–60; [PDF (1480 KB), PDF with Links (1306 KB)]; MR1549920; Zbl 0002.33002 (reviewed by M. Deuring) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 57.0205.01 (reviewed by F. Neiß) [html, DVI, ps, PDF, TeX].

[8] O. Taussky : Eine Verschärfung des Hauptidealsatzes, Jahresber. Deutsch. Math.-Verein. XL (1931), 2. Abt. Heft 6/8, 29–

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[9] W. Schäfer : Beweis des Hauptidealsatzes der Klassenkörpertheorie für den Fall der komplexen Multiplikation, Diss. Halle, 1929, 28 S. (1931); JFM 57.0204.03 (reviewed by F. Neiß) [html, DVI, ps, PDF, TeX].

[10] Ph. Furtwängler : Über die Verschäfung des Hauptidealsatzes für algebraische Zahlkörper, J. Reine Angew. Math. 167 (1932), 379–387; doi: 10.1515/crll.1932.167.379 [PDF (1369 KB)]; PPN243919689_0167_log38 (1,06 MB), GDZ; [PDF], DigiZeitschriften; Zbl 0003.19901 (reviewed by Taussky) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 58.0178.02 (reviewed by A. Scholz) [html, DVI, ps, PDF, TeX].

[11] O. Taussky : Über eine Verschäfung des Hauptidealsatzes für algebraische Zahlkörper, J. Reine Angew. Math. 168 (1932), Heft 4, 193–210; doi: 10.1515/crll.1932.168.193 [PDF (2432

KB)]; PPN243919689_0168_log16.pdf (1,98 MB), GDZ;

[PDF], DigiZeitschriften; Zbl 0006.00803 (reviewed by Deuring) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 58.0178.03 (reviewed by A. Scholz) [html, DVI, ps, PDF, TeX].

[12] K. Taketa : Neuer Beweis eines Satzes von Herrn Furtwängler über die metabelschen Gruppen, Japan. J. Math. [日本數學集報] 9 (1932), 199–218; 9_199.pdf (1299 K), Journal@rchive, JST; Zbl 0006.24504 (reviewed by Taussky) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 58.0126.04 (reviewed by K. Fenchel-Sperling) [html, DVI, ps, PDF, TeX].

[13] J. Herbrand : Sur les théorèmes du genre principal et des idéaux principaux, Abh. Math. Sem. Univ. Hamburg 9 (1933), 84–92; DOI: 10.1007/BF02940630 [xn1115264t637187.pdf (453.6 KB)]; Zbl 0003.29404 (reviewed by Deuring) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 58.0178.01 (reviewed by H. Hasse) [html, DVI, ps, PDF, TeX].

[14] T. Tannaka : Eine Bemerkungen zu den Arbeiten über den allgemeinen Hauptidealsatz, Japan. J. Math. [日本數學集報] 10 (1933), 163–167; 10_163.pdf (390 K), Journal@rchive, JST; Zbl 0011.19703 (reviewed by Taussky) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 59.0945.01 (reviewed by H. Reichardt) [html, DVI, ps, PDF, TeX].

[15] T. Tannaka : Ein Hauptidealsatz relativ-Galoisscher Zahlkörper und ein Satz über den Normenrest, Japan. J. Math. [日本數學集報] 10 (1933), 183–189; 10_183.pdf (457 K), Journal@rchive, JST; Zbl 0009.24401 (reviewed by W. Franz) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 59.0193.01 (reviewed by B. H. Neumann) [html, DVI, ps, PDF, TeX].

[16] T. Tannaka : Über einen Satz von Herrn Artin, Proc. Imp. Acad. [帝國學士院紀事] 9 (1933), No. 5, 197–198; doi:10.3792/pia/1195580808, euclid.pja/1195580808 [PDF (143 KB)]; 9_197.pdf (120 K), Journal@rchive, JST; MR1568342; Zbl 0007.05501 (reviewed by F. K. Schmidt) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 59.0165.03 (reviewed by F. Neisß) [html, DVI, ps, PDF, TeX].

[17] T. Tannaka : Ein Hauptidealsatz relativ-Galoisscher Zahlkörper und ein Satz über den Normenrest, Proc. Imp. Acad. [帝國學士院紀事] 9 (1933), No. 8, 355– 356; doi:10.3792/pia/1195580774, euclid.pja/1195580774 [PDF (102 KB)]; 9_355.pdf (85 K), Journal@rchive, JST; MR1568346; Zbl 0008.05302 (reviewed by Deuring) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 59.0193.01 (reviewed by B. H. Neumann) [html, DVI, ps, PDF, TeX].

[18] S. Iyanaga : Zum Beweis des Hauptidealsatzes, Abh. Math. Sem. Univ. Hamburg 10 (1934), 349–357; DOI: 10.1007/BF02940686 [14267r5395084v62.pdf (431.2 KB)]; reprinted in Shokichi Iyanaga Collected Papers, Iwanami Shoten Publishers, Tokyo, 1994, pp. 44–52; Zbl 0009.19401 (reviewed by Magnus) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 60.0895.01 (reviewed by A. Scholz) [html, DVI, ps, PDF, TeX].

[19] W. Magnus : Über den Beweis des Hauptidealsatzes, J. Reine Angew. Math. 170 (1934), Heft 4, 235– 240; doi: 10.1515/crll.1934.170.235 [PDF (1173 KB)];

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DigiZeitschriften; reprinted in Wilhelm Magnus, collected papers (G. Baumslag and B. Chandler, eds.), Springer, New York, 1983, [6], pp. 97–102; Zbl 0008.24501 (reviewed by Taussky) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 60.0086.03 (reviewed by B. H. Neumann) [html, DVI, ps, PDF, TeX].

[20] A. Scholz und O. Taussky : Die Hauptideale der kubischen Klassenkörper imaginär-quadratischer Zahlörper: ihre rechnerische Bestimmung und ihr Einfluß auf den Klassenkörperturm, J. Reine Angew. Math. 171 (1934), Heft 1, 19–41; doi: 10.1515/crll.1934.171.19 [PDF (3383 KB)];

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[21] E. Witt : Bemerkungen zum Beweis des Hauptidealsatzes von S. Iyanaga, Abh. Math. Sem. Univ. Hamburg 11 (1935), 221; DOI: 10.1007/BF02940724 [h1726368v5j7vq84.pdf (49.3 KB)]; reprinted in Ernst Witt Collected Papers/Gesammelte Abhandlungen edited by I. Kersten with an essay by G. Harder on Witt vector, Springer-Verlag, Berlin, 1998, Class Field Theory and Function Fields, 16, p. 114; Zbl 0014.00701 (reviewed by Magnus) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 62.0084.02 (reviewed by A. Scholz) [html, DVI, ps, PDF, TeX].

[22] H.-G. Schumann : Zum Beweis des Hauptidealsatzes, Abh. Math. Sem. Univ. Hamburg 12 (1937), 42–47; DOI: 10.1007/BF02948931 [e480755u66480573.pdf (290.7 KB)]; Zbl 0016.10301 (reviewed by Magnus) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 63.0066.01 (reviewed W. by Burau) [html, DVI, ps, PDF, TeX].

[23] S. Iyanaga : Über der allgemeinen Hauptidealformeln, Monatsh. Math. Phys. 48 (1939), 400–407; DOI: 10.1007/BF01696195 [jq36086223xv6066.pdf (346.9 KB)]; reprinted in Shokichi Iyanaga Collected Papers, Iwanami Shoten Publishers, Tokyo, 1994, pp. 72–79; MR0000602 (1, 101a) (reviewed by R. Hull) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0063.02999 (not reviewed); JFM 65.0112.03 (reviewed by A. Scholz) [html, DVI, ps, PDF, TeX].

[24] H. Bergström : Vereinfachter Beweis des Hauptidealsatzes der Klassenkörpertheorie, Ark. Mat. Astron. Fys. B 29, (1943), no. 6, 6 pp.; MR0012296 (7, 6b) (reviewed by H. F. Tuan) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0063.00322 (not reviewed).

[25] T. Tannaka and F. Terada : A generalization of the principal ideal theorem, Proc. Japan Acad. [日本學士院紀要] 25 (1949), No. 8, 7–8; doi:10.3792/pja/1195571866, euclid.pja/1195571866 [PDF (140 KB)]; JOI:JST.Journalarchive/pjab1945/25.7 [25_7.pdf (133 K)], Journal@rchive, JST; MR0037839 (12, 316c) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R36-19) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0041.17201 (reviewed by K. G. Ramanathan) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[26] T. Tannaka : An alternative proof of a generalized principal ideal theorem, Proc. Japan Acad. [日本學士院紀要] 25 (1949), No. 11, 26–31; doi:10.3792/pja/1195571871, euclid.pja/1195571871 [PDF (303 KB)]; MR0037842 (12, 316f) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R36-19) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0041.17202 (reviewed by K. G. Ramanathan) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[27] F. Terada : On a generalization of the principal ideal theorem, Tôhoku Math. J. (2) [東北數學雑誌第二輯] 1 (1950), no. 3, 229–269; doi:10.2748/tmj/1178245697, euclid.tmj/1178245697 [PDF (2917 KB)]; 1_229.pdf (3067 K), Journal@rchive, JST; MR0037840 (12, 316d) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R36-19) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0041.17203 (reviewed by P. Roquette) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[28] T. Tannaka : Some remarks concerning principal ideal theorem, Tôhoku Math. J. (2) [東北數學雑誌第二輯] 1 (1950), no. 3, 270–278; doi:10.2748/tmj/1178245698, euclid.tmj/1178245698 [PDF (732 KB)]; 1_270.pdf (733 K), Journal@rchive, JST; MR0037841 (12, 316e) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R36-19) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0041.17301 (reviewed by P. Roquette) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[29] F. Terada : On the principal genus theorem concerning the abelian extensions, Tôhoku Math. J. (2) [東北數學雑誌第二輯] 4 (1952), no. 2, 141–152; doi:10.2748/tmj/1178245416, euclid.tmj/1178245416 [PDF (1127 KB)]; 4_141.pdf (981 K), Journal@rchive, JST; MR0053159 (14, 729a) (reviewed by C. Chevalley; reprinted in Reviews in Number Theory, volume 5, R20-13) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0083.03402 (reviewed by W. Jehne) [scanned image].

[30] H. Kuniyoshi and S. Takahashi : On the principal genus theorem, Tôhoku Math. J. (2) [東北數學雑誌第二輯] 5 (1953), no. 2, 128–131; doi:10.2748/tmj/1178245301, euclid.tmj/1178245301 [PDF (283 KB)]; 5_128.pdf (245 K), Journal@rchive, JST; MR0062172 (15, 938d) (reviewed by G. Hochschild; reprinted in Reviews in Number Theory, volume 5, R38-14) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0052.27402 (reviewed by H. Hasse – W. Jehne) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[31] F. Terada : A note on the principal genus theorem, Tôhoku Math. J. (2) [東北數學雑誌第二輯] 5 (1953), no. 2, 211–213; doi:10.2748/tmj/1178245311, euclid.tmj/1178245311 [PDF (306 KB)]; 5_211.pdf (244 K), Journal@rchive, JST; MR0062173 (15, 938e) (reviewed by G. Hochschild; reprinted in Reviews in Number Theory, volume 5, R38-14) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0052.27403 (reviewed by H. Hasse – W. Jehne) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[32] F. Terada : Complex multiplication and the principal ideal theorem, Tôhoku Math. J. (2) [東北數學雑誌第二輯] 6 (1954), no. 1, 21–25; doi:10.2748/tmj/1178245230, euclid.tmj/1178245230 [PDF (448 KB)]; 6_21.pdf (371 K), Journal@rchive, JST; MR0087705 (19, 396e) (reviewed by Z. I. Borevič; reprinted in Reviews in Number Theory, volume 2, G15-15) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0058.03102 (reviewed by P. Roquette) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[33] F. Terada : On a generalized principal ideal theorem, Tôhoku Math. J. (2) [東北數學雑誌第二輯] 6 (1954), no. 2-3, 95–100; doi:10.2748/tmj/1178245168, euclid.tmj/1178245168 [PDF (566 KB)]; 6_95.pdf (466 K), Journal@rchive, JST; MR0068528 (16, 897a) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R36-31) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0058.03101 (reviewed by M. Moriya) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[34] E. Witt : Verlagerung von Gruppen und Hauptidealsatz, Proceedings of ICM (Amsterdam, 1954), Vol. II, North-Holland, Amsterdam, 1954, pp.

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[35] F. Terada : A generalization of the principal ideal theorem, J. Math. Soc. Japan [日本数学会欧文誌] 7 (1955), Supplement, 530–536; doi:10.2969/jmsj/00750530, euclid.jmsj/1261413404 [PDF (554 KB)]; JOI:JST.Journal archive/jmath1948/7.Supplement 530 [7_530.pdf (254 K)], Journal@rchive, JST; MR0083011 (18, 644b) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R38-21) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0068.03401 (reviewed by W. Jehne) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[36] K. Iwasawa : A note on the group of units of an algebraic number field, J. Math. Pure Appl. (9) 35 (1956), 189– 192; reprinted in Kenkichi Iwasawa Collected Papers (G. Fujisaki, K. Kato, M. Kurihara, and S. Nakajima, eds.), Vol. I, Springer-Verlag, Tokyo, 2001, [31], pp. 368–371; MR0076803 (17, 946h) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R22-12) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0071.26504 (reviewed by H. W. Leopoldt) [scanned image].

[37] T. Tannaka : On the generalized principal ideal theorem, Proceedings of the International Symposium on Algebraic number theory, Tokyo & Nikko, 1955, Science Council of Japan, Tokyo, 1956, pp. 65–70; MR0083010 (18, 644a) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R38-20) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0073.26302 (reviewed by P. Popovici) [scanned image].

[38] F. Terada : A generalization of the principal ideal theorem, On the generalized principal ideal theorem, Proceedings of the International Symposium on Algebraic number theory, Tokyo & Nikko, 1955, Science Council of Japan, Tokyo, 1956, pp. 264–265; MR0083479 (18, 714f) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R38-22) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0074.26504 [scanned image].

[39] �� �� ������� : [On the proof of the principal ideal theorem ] (Russian), Vestnik Leningrad. Univ. 12 (1957), no. 13, 5– 8; MR0101255 (21 #68, #4182) (reviewed by R. A. Good; reprinted in Reviews in Number Theory, volume 5, R36-34,

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[40] T. Tannaka : A generalized principal ideal theorem and a proof of conjecture of Deuring, Ann. of Math. (2) 67 (1958), No. 3, 574–589; doi:10.2307/1969872 [PDF (854 KB)], JS-TOR; MR0098727 (20 #5182) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R38-27) [html, PDF, DVI, PostScript, BibTeX].

[41] H. Reichardt : Ein Beweis des Hauptidealsatzes für imaginärquadratische Zahlkörper, Math. Nachr. 17 (1958), Issue 1-6, 318–329; DOI: 10.1002/mana.19580170316 [PDF (514 K)]; MR0123564 (23 #A889) (reviewed by A. Weil; reprinted in Reviews in Number Theory, volume 2, G15-18) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0124.02403 (reviewed by T. Kubota) [scanned image].

[42] H. Kempfert : Zum allgemeinen Hauptidealsatz. I, J. Reine Angew. Math. 210 (1962), Heft 1/2, 38– 64; doi: 10.1515/crll.1962.210.38 [PDF (2535 KB)];

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[43] T. Hsü : Über den Hauptidealsatz für imaginär-quadratische Zahlkörper, J. Reine Angew. Math. 212 (1963), Heft 1/2, 49–62; doi: 10.1515/crll.1963.212.49 [PDF (1736 KB)];

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[44] S. Takahashi : An explicit representation of the generalized principal ideal theorem for the rational ground field, Tôhoku Math. J. (2) [東北數學雑誌第二輯] 16 (1964), no. 2, 176–182; doi:10.2748/tmj/1178243703, euclid.tmj/1178243703 [PDF (315 KB)]; 16_176.pdf (303 K), Journal@rchive, JST; MR0186657 (32 #4115) (reviewed by G. Whaples; reprinted in Reviews in Number Theory, volume 5, R36-48) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0124.02402 (reviewed by T. Kubota) [scanned image].

[45] S. Takahashi : On Tannaka-Terada’s principal ideal theorem for the rational ground field, Tôhoku Math. J.

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[46] H. Kempfert : Zum allgemeinen Hauptidealsatz II, J. Reine Angew. Math. 223 (1966), 28–55; doi: 10.1515/crll.1966.223.28 [PDF (2433 KB)]; PPN243919689_ 0223_log6.pdf (2,11 MB), GDZ; [PDF], DigiZeitschriften; MR0215814 (35 #6649) (reviewed by K. Masuda; reprinted in Reviews in Number Theory, volume 5, R38-42) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0142.29803 (reviewed by Chr. U. Jensen) [scanned image].

[47] Y. Kawada : A remark on the principal ideal theorem, J. Math. Soc. Japan [日本数学会欧文誌] 20 (1968), Nos. 1-2, 166–169; doi:10.2969/jmsj/02010166, euclid.jmsj/1260463301 [PDF (396 KB)]; JOI:JST.Journalarchive/jmath1948/20.166 [20_166.pdf (318 K)], Journal@rchive, JST; MR0223336 (36 #6384) (reviewed by S. Yuan; reprinted in Reviews in Number Theory, volume 5, R38-46) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0191.33701 (reviewed by S. Takahashi) [scanned image].

[48] O. Taussky : A remark concerning Hilbert’s theorem 94, J. Reine Angew. Math. 239/240 (1969), 435– 438; doi: 10.1515/crll.1969.239-240.435 [PDF (635 KB)];

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[73] B. Schmithals : Zur Berechnung der Kapitulation in bikubischen Zahlkörpern, Manuscripta Math. 52 (1985), fasc. 1-3, 171–202; DOI: 10.1007/BF01171491 [rn22071766069q23.pdf

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[99] 三宅克哉 [Miyake, K.] : 類数とイデアル類群–古くて新しい手法–, 代数的整数論とその周辺 [Algebraic Number Theory and Related Topics] (京都大学数理解析研究所, 1997) (伊原康隆編), 数理解析研究所講究録 [RIMS Kokyuroku] 1026, 1998, pp. 1–11; 1026-1.pdf; 1026-1.pdf (1.22 MB), URI: http://hdl.handle.net/2433/61775; MR1647349 (not be reviewed); Zbl 1016.11538 (not reviewed).

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[103] K. W. Gruenberg et A. Weiss : Capitulation and transfer kernels, J. Théor. Nombres Bordeaux 12 (2000), Fasc. 1, 219– 226; doi: 10.5802/jtnb.276 [JTNB_2000__12_1_219_0.pdf];

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[104] C. Thiebaud : Sur la capitulation dans les corps de genres d’une extension abelienne d’un corps quadratique imaginaire, J. Number Theory 85 (2000), no. 1, 92– 107; doi:10.1006/jnth.2000.2550 [PDF (239 K)]; MR1800304 (2001m:11188) (reviewed by E. J. Gomez-Ayala) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1081.11514 [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[105] A. Azizi : Sur la capitulation des 2-classes d’idéaux de 𝕜 = ℚ (\sqrt{2pq}, i) où p ≡ −q ≡ 1 mod 4, Acta Arith. XCIV (2000), fasc. 4, 383–399; aa9445.pdf, icm; MR1779950 (2001k:11221) (reviewed by J.-F. Jaulent) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 0953.11033 (reviewed by F. Soriano-Gafiuk) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[106] M. Kolster and A. Movahhedi : Galois co-descent for etale wild kernels and capitulation, Ann. Inst. Fourier (Grenoble) 50 (2000), Fasc. 1, 35–65; doi: 10.5802/aif.1746

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[107] C. Khare and D. Prasad : On the Steinitz module and capitulation of ideals, Nagoya Math. J. 160 (2000), 1– 15; euclid.nmj/1114631498 [PDF (135 KB)]; MR1804137 (2001k:11229) (reviewed by A. Azizi) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0971.11055 (reviewed by W. Narkiewicz) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[108] A. Azizi : Capitulation of 2-ideal classes of Q(\sqrt{p_{1}p_{2}}, i) where p_{1} and p_{2} are primes such that p_{1} ≡ 1 (mod 8), p_{2} ≡ 5 (mod 8) and ( \frac{p_{1}}{p_{2}} ) = −1, Algebra and number theory (Fez) (M. Boulagouaz and J.-P. Tignol, eds.), Lecture Notes in Pure and Appl. Math., vol. 208, Dekker, New York, 2000, pp. 13–19; [ebook]; MR1724671 (2000h:11118) (reviewed by F. Lemmermeyer) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1003.11050 (reviewed by C. Parry) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

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[112] A. Azizi : Sur une question de capitulation, Proc. Amer. Math. Soc. 130 (2002), no. 8, 2197–2202; DOI: 10.1090/S0002-9939-02-06424-9 [PDF]; doi:10.2307/2699451 [PDF (201 KB)], JSTOR; MR1897477 (2003a:11144) (reviewed by A. Mouhib) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1010.11061 (reviewed by F. Soriano-Gafiuk) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

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[114] A. Azizi et A. Mouhib : Capitulation des 2-classes d’idéaux de ℚ(\sqrt{2}, \sqrt{d}) où d est un entier naturel sans facteurs carrés, Acta Arith. 109 (2003), fasc. 1, 27–63; doi:10.4064/aa109-1-2 [pdf_aa109-1-02.pdf (299.72 Kb)]; MR1980850 (2004f:11121) (reviewed by J.-F. Jaulent) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1077.11078 (reviewed by B. Sodaïgui) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[115] S.-I. Katayama : On class number one composita of real quadratic fields of Chowla-Yokoi type, Proceedings of the 2003 Nagoya Conference “Yokoi-Chowla Conjecture and Related Problems” (Nagoya, 2003) (S.-I. Katayama, C. Levesque and T. Nakahara, eds.), Saga Univ., Saga, 2004, pp. 51–58; MR2109022 (2005i:11160) (reviewed by S. Louboutin) [html, PDF, DVI, PostScript, BibTeX].

[116] A. Azizi et A. Mouhib : Capitulation des 2-classes d’idéaux de certains corps biquadratiques dont le corps de genres differe du 2-corps de classes de Hilbert, Pacific J. Math. 218 (2005), No. 1, 17–36; doi:10.2140/pjm.2005.218.17 [pjm-v218-n1-p02-s.pdf]; MR2224587 (2007c:11127) (reviewed by E. J. G. Ayala) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1152.11345 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[117] A. Azizi et I. Benhamza : Sur la capitulation des 2-classes d’idéaux de ℚ(\sqrt{d}, \sqrt{2}), Ann. Sci. Math. Québec 29 (2005), no. 1, 1–20; 001-020.pdf; MR2296826 (2008e:11130) (reviewed by J.-F. Jaulent) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1217.11097 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[118] M. C. Ismaili et R. El Mesaoudi : Sur la capitulation des 3-classes d’idéaux de la clôture normale de certains corps cubiques purs, Ann. Sci. Math. Québec 29 (2005), no. 1, 49–72; 049-072.pdf; MR2296830 (2008c:11144) (reviewed by D. C. Mayer) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1217.11095 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[119] A. Azizi : Group theory and the capitulation problem for certain biquadratic fields, Proceedings of the International Conference on Mathematics and its Applications (ICMA 2004), (S. L. Kalla et al., eds.), Kuwait Univ. Dep. Math. Comput. Sci., Kuwait, 2005, pp. 43–51; MR2143048 (2006c:11124) (reviewed by E. J. G. Ayala) [html, PDF, DVI, PostScript, Bib-TeX]; Zbl 1075.11072 (reviewed by E. Benjamin) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[120] R. Schertz : On the generalized principal ideal theorem of complex multiplication, J. Théor. Nombres Bordeaux 18 (2006), Fasc. 3, 683–691; doi: 10.5802/jtnb.566

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[122] A. Azizi et M. Talbi : Capitulation des 2-classes d’idéaux de certains corps biquadratiques cycliques, Acta Arith. 127 (2007), fasc. 3, 231–248; doi:10.4064/aa127-3-3 [pdf_aa127-3-03.pdf (218.27 Kb)]; MR2310345 (2008g:11188) (reviewed by E. Jesús Gómez Ayala) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1169.11049 (summary) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

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[124] C. D. González-Avilés : Capitulation, ambiguous classes and the cohomology of the units, J. Reine Angew. Math. 613 (2007), 75–97; DOI: 10.1515/CRELLE.2007.092 [PDF (196.6 KB), PDF with Links (204 KB)]; MR2377130 (2008m:11222) (reviewed by T. Nguyen-Quang-Do) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1226.11122 (reviewed by T. Nguyen Quang Do) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[125] A. Bandini : Greenberg’s conjecture and capitulation in ℤ_{p}^{d}- extensions, J. Number Theory 122 (2007), no. 1, 121–134; doi:10.1016/j.jnt.2006.04.004 [PDF (166 K)]; MR2287114 (2007j:11150) (reviewed by T. Nguyen-Quang-Do) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1106.11037 (reviewed by T. Metsänkylä) [html, PDF, XML, ASCII, DVI, PS, Bib-TeX].

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[127] A. Azizi et M. Taous : Capitulation of 2-ideal classes of k = ℚ(\sqrt{2p}, i) in the genus field of k where p is prime such that p ≡ 1 mod 8, Int. J. Pure Appl. Math. 35 (2007), No. 4, 481–487; 6.pdf; MR2311554 (no review); Zbl 1169.11047 (reviewed by P. Buckingham) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[128] A. Azizi et M. Taous : Capitulation des 2-classes d’idéaux de k = ℚ(\sqrt{2p}, i), Acta Arith. 131 (2008), fasc. 2, 103–123; doi:10.4064/aa131-2-1 [pdf_aa131-2-01.pdf (332.44 Kb)]; MR2388046 (2009c:11178) (reviewed by E. J. G. Ayala) [html, PDF, DVI, PostScript, BibTeX]; Zbl 1139.11048 (reviewed by F. Nicolae) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

[129] A. Azizi et M. Talbi : Capitulation des 2-classes d’idéaux de Q(\sqrt{−pq(2 + \sqrt{2})}) où p ≡ q ≡ 5 mod 8, Annal. Math. Blaise Pascal 16 (2009), no. 1, 57– 69; doi: 10.5802/ambp.253 [AMBP_2009__16_1_57_0.pdf];

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[132] 田谷久雄 : 代数体の capitulation 問題についての注意, 第 9 回北陸数論研究集会報告集 [Proceedings of the 9th Workshop on Number Theory] (金沢大学サテライトプラザ, 2010) (平林幹人, 野村明人, 山下浩, 木村巌, 菅野孝史編), 2011, pp. 111–124.