Galois theory and the existence of maximal unramified subalgebras

Kreimer, H. F.

doi:10.1090/S0002-9939-1975-0352074-X

Galois theory and the existence of maximal unramified subalgebras
HTML articles powered by AMS MathViewer

by H. F. Kreimer

Proc. Amer. Math. Soc. 47 (1975), 45-48

DOI: https://doi.org/10.1090/S0002-9939-1975-0352074-X

PDF | Request permission

Abstract:

Let $B$ be a commutative ring with 1, let $G$ be a finite group of automorphisms of $B$, and let $A$ be the subring of $G$-invariant elements of $B$. There exists a $G$-stable, unramified $A$-subalgebra of $B$ which contains every unramified $A$-subalgebra of $B$.

References

M. Auslander and D. A. Buchsbaum, On ramification theory in noetherian rings, Amer. J. Math. 81 (1959), 749–765. MR 106929, DOI 10.2307/2372926
Maurice Auslander and Oscar Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409. MR 121392, DOI 10.1090/S0002-9947-1960-0121392-6
N. Bourbaki, Éléments de mathématique. Fasc. XXXI. Algèbre commutative. Chapitre 7: Diviseurs, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1314, Hermann, Paris, 1965 (French). MR 0260715
Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
S. U. Chase, D. K. Harrison, and Alex Rosenberg, Galois theory and Galois cohomology of commutative rings, Mem. Amer. Math. Soc. 52 (1965), 15–33. MR 195922
O. E. Villamayor and D. Zelinsky, Galois theory for rings with finitely many idempotents, Nagoya Math. J. 27 (1966), 721–731. MR 206055

Bibliographic Information

Journal: Proc. Amer. Math. Soc. 47 (1975), 45-48
DOI: https://doi.org/10.1090/S0002-9939-1975-0352074-X
MathSciNet review: 0352074