$\mathcal{GP}$-Projective and $\mathcal{GI}$-Injective Modules

Q. X. Pan^ab, X. L. Zhu<sup>ab

a</sup> Nanjing Agricultural University, China
^b Nanjing University, China

Abstract: Let $R$ be a ring. This paper introduces and studies $\mathcal{GP}$-projective and $\mathcal{GI}$-injective left $R$-modules. Our main goal is to investigate the “global” dimension
$$ \operatorname{GPID}(R)=\sup\{\operatorname{id}(M)\mid M\in{_R\mathcal{M}},\,\text{$M$ is Gorenstein projective}\}. $$


Keywords: Gorenstein dimension, $\mathcal{GP}$-projective module, $\mathcal{GI}$-injective module, left-$\operatorname{GPI}$ ring, semisimple ring.

UDC: 512.533

Received: 20.09.2011

DOI: 10.4213/mzm9390

 English version: Mathematical Notes, 2012, 91:6, 824–832

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