Strongly W-Gorenstein modules

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 modules. As applications, many known results are generalized.