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GORENSTEIN HOMOLOGICAL PROPERTIES OF TENSOR RINGS

Published online by Cambridge University Press:  07 June 2018

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 [email protected]
MING LU
Affiliation:
Department of Mathematics, Sichuan University, Chengdu 610064, PR China email [email protected]

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.

Type
Article
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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