Displaying similar documents to “On finitely generated n-SG-projective modules”

The existence of relative pure injective envelopes

Fatemeh Zareh-Khoshchehreh, Kamran Divaani-Aazar (2013)

Colloquium Mathematicae

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Let 𝓢 be a class of finitely presented R-modules such that R∈ 𝓢 and 𝓢 has a subset 𝓢* with the property that for any U∈ 𝓢 there is a U*∈ 𝓢* with U* ≅ U. We show that the class of 𝓢-pure injective R-modules is preenveloping. As an application, we deduce that the left global 𝓢-pure projective dimension of R is equal to its left global 𝓢-pure injective dimension. As our main result, we prove that, in fact, the class of 𝓢-pure injective R-modules is enveloping.

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...