Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Automorphisms of commutative rings


Author: H. F. Kreimer
Journal: Trans. Amer. Math. Soc. 203 (1975), 77-85
MSC: Primary 13B10
DOI: https://doi.org/10.1090/S0002-9947-1975-0396521-0
MathSciNet review: 0396521
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $B$. For any separable $A$-subalgebra $A’$ of $B$, the following assertions are proved: (1) $A’$ is a finitely generated, protective $A$-module; (2) for each prime ideal $p$ of $A$, the rank of ${A’_p}$ over ${A_p}$ does not exceed the order of $G$; (3) there is a finite group $H$ of automorphisms of $B$ such that $A’$ is the subring of $H$-invariant elements of $B$. If, in addition, $A’$ is $G$-stable, then every automorphism of $A’$ over $A$ is the restriction of an automorphism of $B$, and ${\operatorname {Hom} _A}(A’,A’)$ is generated as a left $A’$-module by those automorphisms of $A’$ which are the restrictions of elements of $G$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 13B10

Retrieve articles in all journals with MSC: 13B10


Additional Information

Keywords: Automorphism, commutative ring, Galois extension
Article copyright: © Copyright 1975 American Mathematical Society