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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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