Abstract:

The strongly Ω-Gorenstein injective modules are defined and the properties of strongly Ω-Gorenstein injective modules are discussed by homological method. Some examples are given to show that the class of Ω-Gorenstein injective modules contains the class of strongly Ω-Gorenstein injective modules. At last, it is proved that M is Ω-Gorenstein injective modules if and only if M is a direct summand of a strongly Ω-Gorenstein injective modules.

Key words: strongly Gorenstein injective modules; Ω-Gorenstein injective modules; strongly Ω-Gorenstein injective modules