关于Gorenstein cotorsion模

On Gorenstein Cotorsion Modules

讨论了Gorenstein cotorsion模与内射模之间的关系,证明了R是Gorenstein von Neumann正则环当且仅当任意R-模M的Gorenstein cotorsion包络与内射包络是同构的,当且仅当E(M)/M是Gorenstein平坦模.同时,也讨论了Gorenstein cotorsion模与cotorsion模之间的联系.

We investigated the relations between Gorenstein cotorsion and injective modules, and proved that a ring R is Gorenstein yon Neumann regular if and only if the Gorenstein cotorsion envelope and injective envelope of any Rmodule M are isomorphism, if and only if E（M）/M is Gorenstein flat Rmodule. Meanwhile, the connections between Gorenstein cotorsion and cotorsion modules are discussed as well.