General RM rings

Abstract EN

The concept of central RM rings is introduced in this paper as a generalization of RM rings.

Since every RM ring is central RM we study the sufficient condition for a central RM ring to be a RM one.

It is shown that every central reversible and hence every central symmetric is central RM ring, however converse implications are wrong.

It is also proven that the polynomial ring R[x] is central RM ring if R is central RM and quasi-Armendariz.

Also -RM ring has been studied with it is central.