On a generalization of NC-McCoy Rings

TL;DR

This paper introduces and studies J-McCoy rings, a generalization of NC-McCoy rings, exploring their properties, examples, and how the property behaves under certain ring constructions.

Contribution

It defines J-McCoy rings, proves that local rings are J-McCoy, and characterizes J-McCoy rings in abelian rings, including behavior under matrix and subring constructions.

Findings

Local rings are J-McCoy.

J-McCoy property does not pass to Mn(R).

Certain subring and matrix constructions are J-McCoy.

Abstract

In the present paper we concentrate on a natural generalization of NC-McCoy rings that is called J-McCoy and investigate their properties. We prove that local rings are J-McCoy. Also, for an abelian ring R, we show that R is J-McCoy if and only if eR is J-McCoy, where e is an idempotent element of R. Moreover, we give an example to show that the J-McCoy property does not pass Mn(R), but S(R; n);A(R; n);B(R; n) and T(R; n) are J-McCoy