Displaying similar documents to “ λ and μ -dimensions of modules”

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.

Strongly 𝒲 -Gorenstein modules

Husheng Qiao, Zongyang Xie (2013)

Czechoslovak Mathematical Journal

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Let 𝒲 be a self-orthogonal class of left R -modules. We introduce a class of modules, which is called strongly 𝒲 -Gorenstein modules, and give some equivalent characterizations of them. Many important classes of modules are included in these modules. It is proved that the class of strongly 𝒲 -Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly 𝒲 -Gorenstein module can be inherited by its submodules and quotient...

Copure injective resolutions, flat resolvents and dimensions

Edgar E. Enochs, Jenda M. G. Overtoun (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize n -Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring R has cokernels (respectively kernels), then R is 2 -Gorenstein.

The existence of envelopes

Edgar E. Enochs, Overtoun M. G. Jenda, Jinzhong Xu (1993)

Rendiconti del Seminario Matematico della Università di Padova

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