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arXiv · 1609.00944

Armendariz ring with weakly semicommutativity

Sushma Singh·Om Prakash
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Abstract

In this article, we introduce the weak ideal-Armendariz ring which combines Armendariz ring and weakly semicommutative properties of rings. In fact, it is a generalisation of an ideal-Armendariz ring. We investigate some properties of weak ideal Armendariz rings and prove that R is a weak ideal-Armendariz ring if and only if R[x] is weak ideal-Armendariz ring. Also, we generalise weak ideal-Armendariz as strongly nil-IFP and a number of properties are discussed which distinguishes it from other existing structures. We prove that if I is a semicommutative ideal of a ring R and R/I is a strongly nil-IFP, then R is strongly nil-IFP. Moreover, if R is 2-primal, then R[x]/ is a strongly nil-IFP.

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Sushma Singh, Om Prakash. 2016-09-04. Armendariz ring with weakly semicommutativity. https://arxiv.org/abs/1609.00944

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