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2018 Semidualizing Module and Gorenstein Homological Dimensions
Zhen Zhang
Afr. Diaspora J. Math. (N.S.) 21(1): 73-80 (2018).

Abstract

Let $C$ be a semidualizing module over any commutative ring $R$. We investigate the semidualizing module $C$ with finite injective dimension. In particular, we obtain some equivalent characterizations of $C$ under the trivial extension of $R$ by $C$. Moreover, we get that the supremum of the $C$-Gorenstein projective dimensions of all $R$-modules and the supremum of the $C$-Gorenstein injective dimensions of all $R$-modules are equal. Hence the $C$-Gorenstein global dimension of the ring $R$ is definable. At last, we consider the weak $C$-Gorenstein global dimension.

Citation

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Zhen Zhang. "Semidualizing Module and Gorenstein Homological Dimensions." Afr. Diaspora J. Math. (N.S.) 21 (1) 73 - 80, 2018.

Information

Published: 2018
First available in Project Euclid: 9 May 2018

zbMATH: 1401.13041
MathSciNet: MR3796417

Subjects:
Primary: 13D02, 13D05, 13D07

Rights: Copyright © 2018 Mathematical Research Publishers

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Vol.21 • No. 1 • 2018
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