A note on lower nil M-Armendariz rings

Abstract

In this article, we prove some results for lower nil M-Armendariz ring. Let M be a strictly totally ordered monoid and I be a semicommutative ideal of R. If R/I is a lower nil M-Armendariz ring, then R is lower nil M-Armendariz. Similarly, for above M, if I is 2-primal with N_{*}(R) subset of I and R/I is M-Armendariz, then R is a lower nil M-Armendariz ring. Further, we observe that if M is a monoid and N a u.p.-monoid where R is a 2-primal M-Armendariz ring, then R[N] is a lower nil M-Armendariz ring.