Geodesic
$\mathcal{GP}$-Projective and $\mathcal{GI}$-Injective Modules
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 870-879.

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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. 
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Q. X. Pan; X. L. Zhu. $\mathcal{GP}$-Projective and $\mathcal{GI}$-Injective Modules. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 870-879. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a7/

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