Let R be an associative ring with identity and let J(R) denote the Jacobson radical of R. R is said to be semilocal if R/J(R) is Artinian. In this paper we give necessary and sufficient conditions for the group ring RG, where G is an abelian group, to be semilocal.
机构:
Changzhou Univ, Sch Math & Phys, Changzhou, Jiangsu 213016, Peoples R ChinaChangzhou Univ, Sch Math & Phys, Changzhou, Jiangsu 213016, Peoples R China
机构:
Univ Penn, David Rittenhouse Lab, Math, 209 South 33rd St, Philadelphia, PA 19104 USAUniv Penn, David Rittenhouse Lab, Math, 209 South 33rd St, Philadelphia, PA 19104 USA