J-McCoy Rings Relative To A Monoid

Abstract

For a ring R and a monoid M, we introduce J -M-McCoy rings which are a generalization of weak M-McCoy and J-McCoy rings and investigate their properties. It is shown that for a u.p.-monoid M if R J(R) is reversible then R is J-M-McCoy, and for a cancellative monoid M and an ideal N of M, R is a right (resp. left) J-M-McCoy ring if it is a right (resp. left) J-N-McCoy ring.