arXiv subjects

Sushma Singh

Publications and source records attributed to Sushma Singh.

5 recordsLinked to original sources

arXiv2022

New Results on Generalization of Jordan centralizers over matrix rings

This paper presents a study on Jordan maps over matrix rings with some functional equations related to additive maps on these rings. We first show that every Jordan left (right) centralizer over a matrix ring is a left (right) centralizer. Moreover, every two-sided centralizer over the matrix ring is of a particular form. Further, we prove that any additive map satisfying functional equations over matrix rings becomes a two-sided centralizer. Finally, we conclude our work with some results on the Jordan left $\star$- centralizer over matrix rings and establish some results on functional equations that arise for the $\star$-centralizer.

math.RA↗

arXiv2018

A note on lower nil M-Armendariz rings

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.

math.RA↗

arXiv2018

Armendariz ring with weakly semicommutativity

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.

math.RA↗

arXiv2017

Extension of Almost Armendariz Rings

A ring $R$ is said to be an almost Armendariz ring if whenever product of two polynomials in $R[x]$ is zero, then product of their coefficients are in $N_{*}(R)$. In this article, for an endomorphism $α$ on $R$, we define an $α$-almost Armendariz ring of $R$ considering the polynomials in skew polynomial ring $R[x; α]$ instead of $R[x]$. It is the generalisation of an almost Armendariz ring [9] and an $α$-Armendariz ring [4]. Moreover, for an endomorphism $α$ of $R$, we define an $α$-skew almost Armendariz ring, and prove that a reversible ring $R$ with certain condition on endomorphism $α$, its polynomial ring $R[x]$ is an $\overlineα$-skew almost Armendariz ring.

math.RA↗

arXiv2017

On Almost Armendariz Rings

In this paper, we introduce the notion of almost Armendariz ring which is the generalization of Armendariz ring and discuss some of its properties. We prove that a ring R is almost Armendariz if and only if n X n upper triangular matrix ring T_{n}(R) is almost Armendariz ring. Similarly, If R is almost Armendariz if and only if R[x] is almost Armendariz. It is observed that every almost Armendariz ring is weak Armendariz but converse need not be true. But, if R is semicommutative ring, then weak Armendariz ring is almost Armendariz ring. Moreover, the class of minimal noncommutative almost Armendariz rings is completely determined, up to isomorphism (minimal means having smallest cardinality).

math.RA↗