Tohoku Mathematical Journal

Some arithmetical applications of groups $H^{q}(R,\,G)$

Akira Hattori

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 33, Number 1 (1981), 35-63.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178229493

Digital Object Identifier
doi:10.2748/tmj/1178229493

Mathematical Reviews number (MathSciNet)
MR0613107

Zentralblatt MATH identifier
0476.12009

Subjects
Primary: 12A60
Secondary: 12G05: Galois cohomology [See also 14F22, 16Hxx, 16K50] 13D05: Homological dimension

Citation

Hattori, Akira. Some arithmetical applications of groups $H^{q}(R,\,G)$. Tohoku Math. J. (2) 33 (1981), no. 1, 35--63. doi:10.2748/tmj/1178229493. https://projecteuclid.org/euclid.tmj/1178229493


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References

  • [1] E. ARTIN AND J. TATE, Class Field Theory, Benjamin, New York, 1967.
  • [2] S. U. CHASE, D. K. HARRISON AND A. ROSENBERG, Galois theory and Galois cohomolog of commutative rings, Memoirs Amer. Math. Soc. 52 (1965), 15-33.
  • [3] D. A. GARBANATI, The Hasse norm theorem for non-cyclic extensions of the rationale, Proc. London Math. Soc. 37 (1978), 143-164.
  • [4] F. GERTH III, The Hasse norm principle in cyclotomic number fields, J. reine angew Math. 303/4 (1978), 249-252.
  • [5] S. GURAK, On the Hasse norm principle, ibid. 299 (1978), 16-27
  • [6] S. GURAK, Hasse norm principle in non-abelian extensions, ibid. 303/4 (1978), 314-317
  • [7] A. HATTORI, On exact sequences of Hochschild and Serre, J. Math. Soc. Japan 7 (1955), 312-321.
  • [8] A. HATTORI, On groups Hn(S, G) and the Brauer group of commutative rings, Sci. Pap Coll. Gen. Educ. Univ. Tokyo 28 (1978), 1-20.
  • [9] A. HATTORI, On groups Hn(SIR) related to the Amitsur cohomology and the Braue group of commutative rings, Osaka J. Math. 16 (1979), 357-382.
  • [9a] A. HATTORI, On Amitsur cohomology of rings of algebraic integers, to appear
  • [10] G. HOCHSCHILD AND J. -P. SERRE, Cohomology of group extensions, Trans. Amer. Math Soc. 74 (1953), 110-134.
  • [11] K. IWASAWA, A note on class numbers of algebraic number fields, Abh. Math. Sem Univ. Hamburg 20 (1956), 257-258.
  • [12] K. IWASAWA, A note on the group of units of an algebraic number field, J. Math, pure et appl. 35 (1956), 189-192.
  • [13] K. IWASAWA, On the theory of cyclotomic fields, Ann. Math. 70 (1959), 530-561
  • [14] K. IWASAWA, On ^-extensions of algebraic number fields, ibid. 98 (1973), 246-326
  • [15] S. IYANAGA AND T. TAMAGAWA, Sur la theorie du corps de classes sur le corps de nombre rationnels, J. Math. Soc. Japan 3 (1951), 220-227.
  • [16] H. W. LEOPOLDT, Zur Geschlechtertheorie in abelschen Zahlkorpern, Math. Nachr. (1953), 351-362.
  • [17] S. MAGLANE, Group extensions by primary abelian groups, Trans. Amer. Math. Soc. 9 (1960), 1-16.
  • [18] T. NAKAYAMA, A remark on fundamental exact sequences in cohomology of finite groups, Proc. Japan Acad. 32 (1956), 731-735.
  • [19] M. J. RAZAR, Central and genus class fields and the Hasse norm theorem, Compositi Math. 35 (1977), 281-298.
  • [20] K. -H. ULBRICH, An abstract version of the Hattori-Villamayor-Zelinsky sequences, Sci Pap.Coll. Gen. Educ. Univ. Tokyo 29 (1979), 125-137.
  • [21] O. E. VILLAMAYOR AND D. ZELINSKY, Brauer groups and Amitsur cohomology for genera commutative ring extensions, J. pure appl. Algebra 10 (1977), 19-55.