Nil-reversible rings

Abstract

This paper introduces and studies nil-reversible rings wherein we call a ring R nil-reversible if the left and right annihilators of every nilpotent element of R are equal. Reversible rings (and hence reduced rings) form a proper subclass of nil-reversible rings and hence we provide some conditions for a nil-reversible ring to be reduced. It turns out that nil-reversible rings are abelian, 2-primal, weakly semicommutative and nil-Armendariz. Further, we observe that the polynomial ring over a nil-reversible ring R is not necessarily nil-reversible in general, but it is nil-reversible if R is Armendariz additionally.

A Note on Skew Generalized Power Serieswise Reversible Property

“…Thus, (f (r )g(t)) dr,t ∈ l k=1 J k = 0, which implies that f (r )g(t) ∈ ni l(R) for all r, t ∈ S. Therefore, we have g(t)f (r ) ∈ ni l(R) as well, and so gf ∈ ni l(R[[S, ω]]) as desired. In [12], A homomorphic image of a ni l-reversible ring may not be ni l-reversible, so as (S, ω)-ni lreversible by the next example. Definition 2.22.…”