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Matematicheskie Zametki, 2012, Volume 91, Issue 6, Pages 870–879
DOI: https://doi.org/10.4213/mzm9390 (Mi mzm9390) 		 
$\mathcal{GP}$-Projective and $\mathcal{GI}$-Injective Modules

Q. X. Panab, X. L. Zhuab

a Nanjing Agricultural University, China
b Nanjing University, China
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DOI: https://doi.org/10.4213/mzm9390
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.
Received: 20.09.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 6, Pages 824–832
DOI: https://doi.org/10.1134/S000143461205029X
Bibliographic databases:
Document Type: Article
UDC: 512.533
Language: Russian
Citation: Q. X. Pan, X. L. Zhu, “$\mathcal{GP}$-Projective and $\mathcal{GI}$-Injective Modules”, Mat. Zametki, 91:6 (2012), 870–879; Math. Notes, 91:6 (2012), 824–832
Citation in format AMSBIB
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