Conditions under which the power series ring is a right gr-ring

Abstract

A right gr-ring is a class of reversible rings that have been the subject of many researches so far. In this paper, we demonstrate if R[[x]] is a right gr-ring, then R is also a right gr-ring. Also, we try to obtain conditions under which R[[x]] is a right gr-ring. For this purpose, we prove that if R is a von Neumann right gr-ring, then R[[x]] is a symmetric ring. Finally, it is asserted that if the power series ring R[[x]] of a von Neumann right gr-ring R is a left self injective ring, then R[[x]] is a right gr-ring. Keywords: right gr-ring, power series, symmetric ring, self injective