A note on lower nil M-Armendariz rings. Issue 1 (1st January 2018) - Singh, Sushma; Prakash, Om
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 ) ⊆ I and R / I is M -Armendariz, then R is a lower nil M -Armendariz ring. Further, we find 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.