TY - JOUR ID - 1437 TI - COTORSION DIMENSIONS OVER GROUP RINGS JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Hajizamani, A. AD - Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandarabbas, Iran. Y1 - 2019 PY - 2019 VL - 7 IS - 1 SP - 25 EP - 32 KW - cotorsion dimension KW - global cotorsion dimension KW - perfect ring DO - 10.22044/jas.2018.7166.1350 N2 - 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 $Z\Gamma$ and $Z\Gamma'$ are equal. UR - https://jas.shahroodut.ac.ir/article_1437.html L1 - https://jas.shahroodut.ac.ir/article_1437_315d3ce1c425b6bc3ed88b4eefa39ca6.pdf ER -