COTORSION DIMENSIONS OVER GROUP RINGS

Let $Gamma$ be a group, $Gamma $ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma $-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma $ are equal.

کلیدواژه ها:

cotorsion dimension ، global cotorsion dimension ، perfect ring