Gorenstein hereditary rings with respect to a semidualizing module

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Hangzhou Dianzi University‎, ‎Hangzhou‎, ‎310018‎, ‎P.R‎. ‎China.

2 School of Mathematics and Information Science‎, ‎Henan Polytechnic University‎, ‎Jiaozuo‎, ‎454000‎, ‎P.R‎. ‎China.

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 over which‎ ‎every submodule of a projective (flat) module is $G_C$-projective (flat)‎, ‎which we call $C$-Gorenstein (semi)hereditary rings‎. ‎It is proved that every $C$-Gorenstein hereditary ring is both coherent and $C$-Gorenstein semihereditary.

Keywords

Main Subjects


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Volume 43, Issue 6
November and December 2017
Pages 1671-1677
  • Receive Date: 03 December 2015
  • Revise Date: 29 August 2016
  • Accept Date: 08 September 2016