English

Abstract

A ring R is called right P-injective if every homomorphism from a principal right ideal of R to RR can be extended to a homomorphism from RR to RR. Let R be a ring and G a group. Based on a result of Nicholson and Yousif, we prove that the group ring RG is right P-injective if and only if (a) R is right P-injective; (b) G is locally finite; and (c) for any finite subgroup H of G and any principal right ideal I of RH, if f ∈ HomR(IR,RR), then there exists g ∈ HomR(RHR,RR) such that gI = f. Similarly, we also obtain equivalent characterizations of n-injective group rings and F-injective group rings.