ON A GENERALIZATION OF WEAK M-ARMENDARIZ RINGS

Abstract

For a ring R and a monoidM, we introduce J-M-Armendariz rings which are a generalization of weak M-Armendariz and J-Armendariz rings, and we investigate their properties. We prove that if R J(R) is a reduced ring and R is a J-M-Armendariz ring, then R is J-M N-Armendariz, where N is a unique product monoid. It is also shown that a nitely generated Abelian group G is torsion free if and only if there exists a ring R such that R is G-J-Armendariz.