Group rings with annihilator conditions

A ring R is called left (Kasch) dual if every (maximal) left ideal of R is a left annihilator. R is left CF if every left ideal of R is the left annihilator of a finite number of elements of R. Let RG be the group ring of a group G over a ring R. It is proved that RG is a left Kasch ring if and only if R is left Kasch and G is finite. Characterizations of left dual (left CF) group rings are also discussed in this article.