A noncommutative generalization of Auslander's last theorem.

Enochs, Edgar E.; Jenda, Overtoun M.G.; López-Ramos, J.A.

Displaying similar documents to “A noncommutative generalization of Auslander's last theorem.”

$C$ -Gorenstein projective, injective and flat modules

Xiao Yan Yang, Zhong Kui Liu (2010)

Czechoslovak Mathematical Journal

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By analogy with the projective, injective and flat modules, in this paper we study some properties of $C$ -Gorenstein projective, injective and flat modules and discuss some connections between $C$ -Gorenstein injective and $C$ -Gorenstein flat modules. We also investigate some connections between $C$ -Gorenstein projective, injective and flat modules of change of rings.

A generalization of the Auslander transpose and the generalized Gorenstein dimension

Yuxian Geng (2013)

Czechoslovak Mathematical Journal

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Let $R$ be a left and right Noetherian ring and $C$ a semidualizing $R$ -bimodule. We introduce a transpose ${Tr}_{c} M$ of an $R$ -module $M$ with respect to $C$ which unifies the Auslander transpose and Huang’s transpose, see Z. Y. Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use ${Tr}_{c} M$ to develop further the generalized Gorenstein dimension with respect to $C$ . Especially, we generalize the Auslander-Bridger formula to...

Characterizations of some rings with $𝒞$ -projective, $𝒞$ -(FP)-injective and $𝒞$ -flat modules

Xiao Guang Yan, Xiao Sheng Zhu (2011)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative ring and $𝒞$ a semidualizing $R$ -module. We investigate the relations between $𝒞$ -flat modules and $𝒞$ -FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.

Cohen-Macaulay homological dimensions

Henrik Holm, Peter Jørgensen (2007)

Rendiconti del Seminario Matematico della Università di Padova

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On presented dimensions of modules and rings.

Zhou, Dexu, Gong, Zhiwei (2010)

International Journal of Mathematics and Mathematical Sciences

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Displaying similar documents to “A noncommutative generalization of Auslander's last theorem.”

C -Gorenstein projective, injective and flat modules

A generalization of the Auslander transpose and the generalized Gorenstein dimension

Characterizations of some rings with 𝒞 -projective, 𝒞 -(FP)-injective and 𝒞 -flat modules

Cohen-Macaulay homological dimensions

On presented dimensions of modules and rings.

$C$ -Gorenstein projective, injective and flat modules

Characterizations of some rings with $𝒞$ -projective, $𝒞$ -(FP)-injective and $𝒞$ -flat modules