代数体の中心拡大に関する文献 (2012 年 2 月更新版)

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[3] A. Scholz : Abelsche Durchkreuzung, Monatsh. Math. Phys. 48 (1939), 340–352; DOI: 10.1007/BF01696190 [u72w67205h114092.pdf (647.8 KB)]; MR0000623 (1, 104c) (reviewed by R. Baer) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0023.21101 (reviewed by J. J. Burckhardt) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften; JFM 65.0066.02 (reviewed by L. Holzer) [html, DVI, ps, PDF, TeX].

[4] A. Scholz : Abelsche Durchkreuzung, J. Reine Angew. Math. 182 (1940), 216; doi: 10.1515/crll.1940.182.216 [PDF (269

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[5] A. Scholz : Totale Normenreste die keine Normes sind, als Erzeugen nichtabelscher Körpererweiterungen. II, J. Reine Angew. Math. 182 (1940), Heft 3/4, 217– 234; doi: 10.1515/crll.1985.182.217 [PDF (3405 KB)];

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[6] A. Fröhlich : On the absolute class group of Abelian fields, J. London Math. Soc. 29 (1954), Part 2, 211–217; doi:10.1112/jlms/s1-29.2.211 [211.full.pdf]; MR0066422 (16 #573a) (reviewed by Y. Kawada; reprinted in Reviews in Number Theory, volume 5, R20-23) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0055.03302 (reviewed by H.- J. Kowalsky) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[7] A. Fröhlich : A remark on the class number of Abelian fields, J. London Math. Soc. 29 (1954), Part 4, 498; doi:10.1112/jlms/s1-29.4.498a [498.full.pdf]; MR0066423 (16 #573b) (reviewed by Y. Kawada; reprinted in Reviews in Number Theory, volume 5, R20-23) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0055.26804 (reviewed by H. Reichardt) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[8] A. Fröhlich : On fields of class two, Proc. London Math. Soc. (3) 4 (1954), 235–256; doi:10.1112/plms/s3-4.1.235 [235.full.pdf]; MR0063404 (16 #116b) (reviewed by H. Bergström; reprinted in Reviews in Number Theory, volume 5, R36-30) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0055.03301 (reviewed by H.-J. Kowalsky) [scanned image]; [PDF], GDZ; [PDF], DigiZeitschriften.

[9] Y. Furuta : Über die zentrale Klassenzahl eines relativ-Galoischen Zahlkörpers, J. Number Theory 3 (1971), no. 3, 318–322; doi:10.1016/0022-314X(71)90007-2 [PDF (221 K)]; MR0297743 (45 #6795) (reviewed by J. Browkin; reprinted in Reviews in Number Theory, volume 5A, R26-202) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0219.12015 (Autorreferat) [scanned image].

[10] 中越矩方 [Nakagoshi, N.] : On the class number of a Galois extension, 解析的整数論 [Analytic Number Theory] (竜沢周雄編), 数理解析研究所講究録 [RIMS Kokyuroku] 193, 1973, 125–128; 0193-9.pdf; 0193-9.pdf (186.87 kB), URI: http://hdl.handle.net/2433/107272.

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[12] M. J. Razar : Central and genus class fields and Hasse norm theorem, Compositio Math. 35 (1977), Fasc. 3, 281–298;

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[13] S. Shirai : On the central class field mod 𝔪 of Galois extension of an algebraic number field, Nagoya Math. J. 71 (1978), 61–85; euclid.nmj/1118785604 [PDF (1825 KB)]; MR0508995 (80c:12015) (reviewed by J. Browkin; reprinted in Reviews in Number Theory, volume 5A, R38-228) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0362.12009 (Autorreferat) [scanned image].

[14] S. Shirai : On the Galois groups of class two extensions over the rational number field, Nagoya Math. J. 75 (1979), 121– 131; euclid.nmj/1118785867 [PDF (732 KB)]; MR0542192 (82f:12003) (reviewed by Y. Furuta; reprinted in Reviews in Number Theory, volume 5A, R38-228F) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0393.12014 (Autorreferat) [scanned image].

[15] S. Shirai : On the central ideal class group of cyclotomic fields, Nagoya Math. J. 75 (1979), 133–143; euclid.nmj/1118785868 [PDF (812 KB)]; MR0542193 (82f:12004) (reviewed by Y. Furuta; reprinted in Reviews in Number Theory, volume 5A, R38-228G) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0393.12007 (Autorreferat) [scanned image].

[16] 白井進, 古田孝臣 : 代数体の中心的拡大について, 第 25 回代数学シンポジウム報告集 (北海道大学, 1979) (森田康夫, 都築俊郎, 近藤武, 土井公二, 岩堀長慶編), 1979, pp. 36–54.

[17] Y. Furuta : A prime decomposition symbol for a nonabelian central extension which is abelian over a bicyclic biquadratic field, Nagoya Math. J. 79 (1980), 79– 109; euclid.nmj/1118786170 [PDF (2207 KB)]; MR0587411 (82a:12008) (reviewed by R. Perlis; reprinted in Reviews in Number Theory, volume 5A, R20-239) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0444.12001 (reviewed by H. Yokoi) [scanned image].

[18] H. Opolka : Zur Auflösung zahlentheoretischer Knoten, Math. Z. 173 (1980), Heft 1, 95–103; DOI: 10.1007/BF01215526 [j1127775835q1538.pdf (514.7 KB)];

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[19] H. Opolka : Auflösung zahlentheoretischer Knoten in Galoiserweiterungen Q, Arch. Math. (Basel) 34 (1980), No. 5, 416–420; DOI: 10.1007/BF01224980 [vh37px35l201xn13.pdf (315.4 KB)]; MR0593768 (82e:12010) (reviewed by P. Damey; reprinted in Reviews in Number Theory, volume 5A, R34-258) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0416.12005 (Autorreferat) [scanned image].

[20] F. P. Heider : Zahlentheoretische Knoten unendlicher Erweiterungen Q, Arch. Math. (Basel) 37 (1981), No. 4, 341–352; DOI: 10.1007/BF01234367 [v53253020t41tr57.pdf (642.4 KB)]; MR0639339 (84i:12006) (reviewed by J. Sonn) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0475.12009 (reviewed by R. J. Stroeker) [scanned image].

[21] H. Opolka : Geschlechter von zentralen Erweiterungen, Arch. Math. (Basel) 37 (1981), No. 5, 418–424; DOI: 10.1007/BF01234376 [t11665ugv33r4482.pdf (356.6 KB)]; MR0643283 (83h:12006) (reviewed by N. Klingen; reprinted in Reviews in Number Theory, volume 5A, R34-265) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0452.12002 (Autorreferat) [scanned image].

[22] 白井進 [Shirai, S.] : ある種のクラス 2 拡大における素イデアル分解について, Z_{p} 拡大およびその関連理論の研究 [Studies on the Z_{P} Extension and Its Neighboring Theory] (京都大学数理解析研究所, 1981) (藤崎源二郎編), 数理解析研究所講究録 [RIMS Kokyuroku] 440, 1981, 131–144; 0440-14.pdf; 0440-14.pdf (900.37 kB), URI: http://hdl.handle.net/2433/102810.

[23] H. Opolka : Some remarks on the Hasse norm theorem, Proc. Amer. Math. Soc. 84 (1982), no. 4, 464–466; DOI: 10.1090/S0002-9939-1982-0643730-8 [PDF]; doi:10.2307/2044016 [PDF], JSTOR; MR0643730 (83h: 12016) (reviewed by P. Damey; reprinted in Reviews in Number Theory, volume 5A, R34-267) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0458.12008 (Autorreferat) [scanned image].

[24] A. Fröhlich : Central extensions, Galois group, and ideal class group of number fields, Comtemporary Mathematics, vol. 24, Amer. Math. Soc., Providence, R. I., 1983, viii + 86 pp.; MR0720859 (85c:11101) (reviewed by L. N. Childs; reprinted in Reviews in Number Theory, volume 5B, R29-631) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0519.12001 (reviewed by H. Opolka) [scanned image].

[25] K. Miyake : Central extensions and Schur’s multiplicators of Galois groups, Nagoya Math. J. 90 (1983), 133– 144; euclid.nmj/1118787181 [PDF (700 KB)]; MR0702256 (84m:12013) (reviewed by A. J. Engler; reprinted in Reviews in Number Theory, volume 5B, R32-613) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0502.12007 (Autorreferat) [scanned image].

[26] 三宅克哉 : 代数的数体のガロア拡大の中心拡大について, 整数論研究集会報告集 (九州大学, 1982) (白谷克己編), 1983, pp. 122–135.

[27] 三宅克哉 : 代数体のイデール群の構造について, 第 29 回代数学シンポジウム報告集 (岩手大学, 1983) (近藤武, 堀田良之, 岩堀長慶, 永田雅宜, 内田興二, 佐々木盛男, 沼田稔, 永尾汎, 藤崎源二郎, 土井公二, 木村浩, 吉田知行, 都築俊郎編), 1983, pp. 307–324.

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[29] Y. Furuta : Supplementary notes on Galois groups of central extensions of algebraic number fields, Sci. Rep. Kanazawa Univ. [金沢大学理科報告] 29 (1984), no.

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[32] E. T. Tan : A remark on Scholz’s abelian crossings, Arch. Math. (Basel) 42 (1984), No. 4, 325–328; DOI: 10.1007/BF01246122 [m0j28381660u421m.pdf (177.1 KB)]; MR0753352 (85j:11149) (reviewed by J. K. Deveny; reprinted in Reviews in Number Theory, volume 5B, R32-626) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0531.12007 (reviewed by H. Opolka) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

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[51] A. Nomura : On the ideal class numbers of certain Hilbert class fields, Manuscripta Math. 79 (1993), fasc. 3–4, 379–390; DOI: 10.1007/BF02568352 [c823hth787706115.pdf (465.9

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[53] T. Crespo : Central extensions of the alternating group as Galois group, Acta Arith. LXVI (1994), fasc. 3, 229– 236; aa6633.pdf, icm; MR1276990 (95f:12008) (reviewed by M. Epkenhaus) [html, PDF, DVI, PostScript, BibTeX]; Zbl 0793.12003 (reviewed by T. Crespo) [html, PDF, XML, ASCII, DVI, PS, BibTeX].

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