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GORENSTEIN HOMOLOGICAL PROPERTIES OF TENSOR RINGS

Part of: Homological methods Homological algebra

Published online by Cambridge University Press:  07 June 2018

XIAO-WU CHEN  and
MING LU
XIAO-WU CHEN
Affiliation:
Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, PR China email xwchen@mail.ustc.edu.cn
MING LU
Affiliation:
Department of Mathematics, Sichuan University, Chengdu 610064, PR China email luming@scu.edu.cn
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Abstract

Let $R$ be a two-sided Noetherian ring, and let $M$ be a nilpotent $R$-bimodule, which is finitely generated on both sides. We study Gorenstein homological properties of the tensor ring $T_{R}(M)$. Under certain conditions, the ring $R$ is Gorenstein if and only if so is $T_{R}(M)$. We characterize Gorenstein projective $T_{R}(M)$-modules in terms of $R$-modules.

MSC classification

Primary: 16E10: Homological dimension 16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 18G25: Relative homological algebra, projective classes
Type
Article
Information
Nagoya Mathematical Journal , Volume 237 , March 2020 , pp. 188 - 208
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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