On a generalization of McCoy Rings

TL;DR

This paper introduces Central McCoy rings, a new generalization of McCoy rings, and explores their properties, including conditions under which polynomial rings and certain matrix subrings are also Central McCoy.

Contribution

It defines Central McCoy rings, establishes their equivalence with polynomial rings, and analyzes their behavior in matrix subrings, expanding the understanding of McCoy ring generalizations.

Findings

R is right Central McCoy iff R[x] is right Central McCoy.

Mn(R) and Tn(R) are not necessarily right Central McCoy.

Dn(R) and Vn(R) are right Central McCoy.

Abstract

We introduce Central McCoy rings, which are a generalization of McCoy rings and investigate their properties. For a ring R, we prove that R is right Central McCoy if and only if the polynomial ring R[x] is right Central McCoy. Also, we give some examples to show that if R is right Central McCoy, then Mn(R) and Tn(R) are not necessary right Central McCoy, but Dn(R) and Vn(R) are right Central McCoy, where Dn(R) and Vn(R) are the subrings of the triangular matrices with constant main diagonal and constant main diagonals, respectively.