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On Galois Extension of Rings

Published online by Cambridge University Press:  22 January 2016

Teruo Kanzaki
Teruo Kanzaki*
Affiliation:
Osaka Gakugei Daigaku
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Let Λ be a ring and G a finite group of ring automorphisms of Λ. The totality of elements of Λ which are left invariant by G is a subring of Λ. We call it the G-fixed subring of Λ. Let be the crossed product of Λ and G with trivial factor set, i.e. {u0} is a Λ-free basis of Δ and , and let Γ be a subring of the G-fixed subring of Λ which has the same identity as Λ.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 43 - 49
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Auslander, M. and Goldman, O.. The Brauer group of a commutative rings, Trans. Amer. Math. Soc. Vol. 97 (1960), 367–409.Google Scholar
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[3] Chase, S. U., Harrison, D. K. and Rosenberg, A., Galois theory and Galois cohomology of commutative rings. Memoirs Amer. Math. Soc. No. 52 (1965).Google Scholar
[4] Kanzaki, T., On commutor ring and Galois theory of separable algebras, Osaka J. Math. Vol. 1 (1964), 103–115.Google Scholar