Geodesic
Strongly $\mathcal {W}$-Gorenstein modules
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 441-449
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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.
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.
DOI : 10.1007/s10587-013-0028-y
Classification : 16D40, 16D50, 16E05, 16E65, 18G20, 18G25
Keywords: self-orthogonal class; strongly $\mathcal {W}$-Gorenstein module; $\mathcal {C}$-resolution 
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     title = {Strongly $\mathcal {W}${-Gorenstein} modules},
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     year = {2013},
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Qiao, Husheng; Xie, Zongyang. Strongly $\mathcal {W}$-Gorenstein modules. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 441-449. doi: 10.1007/s10587-013-0028-y

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