Article
MSC:
16D40,
16D50,
16E05,
16E65,
18G20,
18G25 | MR 3073969 | Zbl 06236422 | DOI: 10.1007/s10587-013-0028-y
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Keywords:
self-orthogonal class; strongly $\mathcal {W}$-Gorenstein module; $\mathcal {C}$-resolution
self-orthogonal class; strongly $\mathcal {W}$-Gorenstein module; $\mathcal {C}$-resolution
Summary:
Let $\mathcal {W}$ be a self-orthogonal class of left $R$-modules. We introduce a class of modules, which is called strongly $\mathcal {W}$-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 $\mathcal {W}$-Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly $\mathcal {W}$-Gorenstein module can be inherited by its submodules and quotient modules. As applications, many known results are generalized.
References:
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