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Science in China Series A: Mathematics

, Volume 51, Issue 2, pp 215–218 | Cite as

Gorenstein flatness and injectivity over Gorenstein rings

  • Song WeiLing 
  • Huang ZhaoYong Email author
Article

Abstract

Let R be a Gorenstein ring. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical. In addition, we prove that if RS is a homomorphism of rings and S E is an injective cogenerator for the category of left S-modules, then the Gorenstein flat dimension of S as a right R-module and the Gorenstein injective dimension of E as a left R-module are identical. We also give some applications of these results.

Keywords

Gorenstein flat Gorenstein injective Gorenstein rings 

MSC(2000)

16E10 16E30 

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Copyright information

© Science in China Press 2008

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingChina

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