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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A change of rings theorem and the Artin-Rees property
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by M. Boratyński
Proc. Amer. Math. Soc. 53 (1975), 307-310
DOI: https://doi.org/10.1090/S0002-9939-1975-0401840-0

Abstract:

A two-sided ideal $\mathfrak {A}$ of the ring $R$ is said to have the left $AR$ property if for every left ideal $I$ and every $k$ there exists an $n$ such that ${\mathfrak {A}^n} \cap I \subset {\mathfrak {A}^k}I$. Let $R$ be a left noetherian ring and $\mathfrak {A}$ a two-sided ideal contained in its Jacobson radical. If $\mathfrak {A}$ has the $\operatorname {AR}$ property then ${\text {l}}\;{\text {gl}}\;{\text {dim}}\;R \leqslant {\text {p}}\;{\text {dim}}\;R/\mathfrak {A} + {\text {l}}\;{\text {gl dim }}R/\mathfrak {A}$, where ${\text {p}}\;{\text {dim}}\;R/\mathfrak {A}$ denotes the (left) projective dimension of the module $R/\mathfrak {A}$.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 53 (1975), 307-310
  • MSC: Primary 16A60
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0401840-0
  • MathSciNet review: 0401840