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Gorenstein flatness and injectivity over Gorenstein rings

Research paper by WeiLing Song, ZhaoYong Huang

Indexed on: 01 Feb '08Published on: 01 Feb '08Published in: Science in China. Series A, Mathematics, physics, astronomy / Chinese Academy of Sciences



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 R → S is a homomorphism of rings and SE 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.