[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c170393

ON U-GROUP RINGS

Osba, Emad Abu (Department of Mathematics School of Science The University of Jordan)
Al-Ezeh, Hasan (Department of Mathematics School of Science The University of Jordan)
Ghanem, Manal (Department of Mathematics School of Science The University of Jordan)

Publication Information

Communications of the Korean Mathematical Society / v.33, no.4, 2018 , pp. 1075-1082 More about this Journal

Abstract

Let R be a commutative ring, G be an Abelian group, and let RG be the group ring. We say that RG is a U-group ring if a is a unit in RG if and only if ${\epsilon}(a)$ is a unit in R. We show that RG is a U-group ring if and only if G is a p-group and $p{\in}J(R)$ . We give some properties of U-group rings and investigate some properties of well known rings, such as Hermite rings and rings with stable range, in the presence of U-group rings.

Keywords

group ring; Hermite ring; rings with stable range; Jacobson radical; p-group;

Citations & Related Records

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