Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An extension of the Noether-Deuring theorem
HTML articles powered by AMS MathViewer

by Klaus W. Roggenkamp PDF
Proc. Amer. Math. Soc. 31 (1972), 423-426 Request permission

Abstract:

Let $R$ be a commutative semilocal noetherian ring, $\Lambda$ a left noetherian $R$-algebra and $M,N$ finitely generated left $\Lambda$-modules such that ${\operatorname {End} _\Lambda }(M)$ is of finite type over $R$. By $\hat R$ we denote the $(\operatorname {rad} R)$-adic completion of $R$. Theorem. $M$ is $\Lambda$-isomorphic to a direct summand of $N$ iff $\hat R{ \otimes _R}M$ is $\hat R{ \otimes _R}\Lambda$-isomorphic to a direct summand of $\hat R{ \otimes _R}N$. This result is used to prove a generalization of the Noether-Deuring theorem. Let $S$ be a commutative $R$-algebra which is a faithful projective $R$-module of finite type; then $M$ is $\Lambda$-isomorphic to direct summand of $N$ iff $S{ \otimes _R}M$ is $S{ \otimes _R}\Lambda$-isomorphic to a direct summand of $S{ \otimes _R}N$.
References
Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 31 (1972), 423-426
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0286839-7
  • MathSciNet review: 0286839