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Strongly \(\mathcal W\)-Gorenstein modules. (English) Zbl 1281.16019
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.

MSC:
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
16D40 Free, projective, and flat modules and ideals in associative algebras
16D50 Injective modules, self-injective associative rings
16E05 Syzygies, resolutions, complexes in associative algebras
18G20 Homological dimension (category-theoretic aspects)
18G25 Relative homological algebra, projective classes (category-theoretic aspects)
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