Gorenstein homological properties of tensor rings

Xiao-Wu Chen; Ming Lu

Gorenstein homological properties of tensor rings

Rings and Algebras 2020-04-14 v1 Representation Theory

Authors: Xiao-Wu Chen , Ming Lu

Abstract

Let $R$ be a two-sided noetherian ring and $M$ 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.

Keywords

gorenstein homological algebra tensor ring noetherian ring nilpotent bimodule gorenstein projective module

Cite

@article{arxiv.1711.06105,
  title  = {Gorenstein homological properties of tensor rings},
  author = {Xiao-Wu Chen and Ming Lu},
  journal= {arXiv preprint arXiv:1711.06105},
  year   = {2020}
}