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Nil Clean Ideal
Ajay Sharma, Dhiren Kumar Basnet
Motivated by the concept of clean ideals, we introduce the notion of nil clean ideals of a ring. We define an ideal of a ring to be nil clean ideal if every element of …
Weakly nil clean graphs of rings
Ajay Sharma, Jayanta Bhattacharyya, Dhiren Kumar Basnet
In this article, the concept of nil clean graph of a ring has been generalised to weakly nil clean graph of a ring and graph theoretic properties like girth, clique number, diamete…
Relative non-commuting graph of a finite ring
Jutirekha Dutta, Dhiren Kumar Basnet
Let be a subring of a finite ring and . The relative non-commuting graph of the subring in , denoted by $Γ_{S, R}…
On non-commuting graph of a finite ring
J. Dutta, D. K. Basnet
The non-commuting graph of a finite ring with center is a simple undirected graph whose vertex set is and two distinct vertices and are…
Weakly -clean rings and weakly -clean rings
Ajay Sharma, Dhiren Kumar Basnet
Motivated by the concept of weakly clean rings, we introduce the concept of weakly -clean rings. We define an element of a ring as weakly -clean if it can be expresse…
Formal triangular matrix ring with nil clean index
Dhiren Kumar Basnet, Jayanta Bhattacharyya
For an element , let $η(a)=\{e\in R\mid e^2=e\mbox{ and }a-e\in \mbox{nil}(R)\}$. The nil clean index of , denoted by NinA, is defined as Nin$(R)=\sup \{\mid η(a)\…