On rings with prime centers.
Let be a finite group , a field of characteristic and let be the group of units in . We show that if the derived length of does not exceed , then must be abelian.
Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
In this paper, we study the situation as to when the unit group U(KG) of a group algebra KG equals K*G(1 + J(KG)), where K is a field of characteristic p > 0 and G is a finite group.
In this paper we consider completely decomposable torsion-free groups and we determine the subgroups which are ideals in every ring over such groups.