关于强Gorenstein FC-投射模

On Strongly Gorenstein FC-Projective Modules

引入强Gorenstein FC-投射模,给出了强Gorenstein FC-投射模的若干等价性质,刻画了右SGFC-半单环.在Morita对偶下,得到了强Gorenstein FC-投射模与强Gorenstein FP-内射模构成了Morita-对偶对,并证明了每个U-自反右R-模都是强Gorenstein FC-投射模当且仅当每个U-自反左S-模都是强Gorenstein FP-内射模.

This paper introduces strongly Gorenstein FC-projective modules,gives some equivalent properties of strongly Gorenstein FC-projective modules,and characterizes right SGFC-semisimple rings. Under Morita-duality,it obtains that strongly Gorenstein FP-injective modules and strongly Gorenstein FC-projective modules forms a Morita-dual pair,and shows that every U-reflexive right R-module is strongly Gorenstein FC-projective if and only if every U-reflexive left S-module is strongly Gorenstein FP-injective.