Gorenstein (semi)hereditary rings with respect to a semidualizing module

Guoqiang Zhao; Juxiang Sun

Gorenstein (semi)hereditary rings with respect to a semidualizing module

Commutative Algebra 2015-01-23 v1

Authors: Guoqiang Zhao , Juxiang Sun

Abstract

Let $C$ be a semidualizing module. We first investigate the properties of finitely generated $G_C$ -projective modules. Then, relative to $C$ , we introduce and study the rings of Gorenstein (weak) global dimensions at most 1, which we call $C$ -Gorenstein (semi)hereditary rings, and prove that every $C$ -Gorenstein hereditary ring is both coherent and $C$ -Gorenstein semihereditary.

Keywords

Gorenstein rings semidualizing module Gorenstein projective modules hereditary rings semihereditary rings global dimension coherent rings

Cite

@article{arxiv.1501.05410,
  title  = {Gorenstein (semi)hereditary rings with respect to a semidualizing module},
  author = {Guoqiang Zhao and Juxiang Sun},
  journal= {arXiv preprint arXiv:1501.05410},
  year   = {2015}
}

Comments

9 pages

Related papers

View all related →