A Note on Skew Generalized Power Serieswise Reversible Property

Abstract

The aim of this paper is to introduce and study (S, ω)-nil-reversible rings wherein we call a ring R is (S, ω)-nil-reversible if the left and right annihilators of every nilpotent element of R are equal. The researcher obtains various necessary or sufficient conditions for (S, ω)-nil-reversible rings are abelian, 2-primal, (S, ω)-nil-semicommutative and (S, ω)-nil-Armendariz. Also, he proved that, if R is completely (S, ω)-compatible (S, ω)-nil-reversible and J an ideal consisting of nilpotent elements of bounded index ≤ n in R, then R/J is (S, ¯ω)-nil-reversible. Moreover, other standard rings-theoretic properties are given.