A Note On Pre-J-Group Rings

Abstract

Given an associative ring R satisfying a°'b = Ba" for any pair a and b of its elements, is being a positive integer, and a group G satisfying x""' = y"~1, we give a sufficient and necessary condition on the group ring GR so that its elements satisfy the same condition assigned to R. A similar result can be obtained if the group G is replaced by a semigroup.