Gorenstein FC_(n)-投射模

Gorenstein FC_(n)-projective modules

设n是一非负整数,引入FC_(n)-投射模和Gorenstein FC_(n)-投射模,并在左n-余凝聚环上讨论了Gorenstein FC_(n)-投射模的同调性质.证明了:若R是左n-余凝聚环且任意有限n-余表示R-模的内射维数有限,则任意R-模是Gorenstein FC_(n)-投射模当且仅当任意循环R-模是Gorenstein FC_(n)-投射模,当且仅当任意内射R-模是FC_(n)-投射模.

Let n be a nonnegative integer,FC_(n)-projective modules and Gorenstein FC_(n)-projective modules are introduced,and the homological properties of the class of Gorenstein FC_(n)-projective modules are investigated on left n-cocoherent rings.It is proved that if R is a n-cocoherent ring and the injective dimension of every finitely n-copresented R-module is finite,then every R-module is Gorenstein FCnprojective,if and only if every cycle R-module is Gorenstein FC_(n)-projective,and if and only if every injective R-module is FC_(n)-projective.