A note on lower nil M-Armendariz rings. Issue 1 (1st January 2018)

• Record Type: Journal Article
• Authors: Singh, Sushma; Prakash, Om
• Editors: Liu, Lishan
• Is Part Of: Cogent mathematics & statistics. Volume 5:Issue 1(2018)
• Publication Date: 2018-01-01
• Subjects: Armendariz ring -- 2-primal ring -- Semicommutative ring -- Skew triangular matrix ring -- u.p.-monoid -- M-Armendariz ring -- Lower nil M-Armendariz ring; 16S36 -- 16N60 -- 16Y99; Mathematics -- Periodicals; Statistics -- Periodicals; Mathematics; Statistics; Periodicals; 510
• DOI: 10.1080/25742558.2018.1545411
• Languages: English
• ISSNs: 2574-2558

Abstract

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.