6 citations · 23 across the 36 of their papers we have counts for
21 papers · 1 filter
Pair of primitive elements in quadratic form with prescribed trace over a finite field
Himangshu Hazarika, Dhiren Kumar Basnet
In this article, we establish a sufficient condition for the existence of primitive element $α\in \Fm$ is such that is also primitive element of $\Fm$ and $Tr_{\Fm/\F}(α)=β$…
Weakly -clean rings
Ajay Sharma, Dhiren Kumar Basnet
In this article, we introduce the concept of weakly -clean ring, for any ideal of a ring . We show that, for an ideal of a ring , is uniquely weakly -clean…
Nil Clean Divisor Graph
Ajay Sharma, Dhiren Kumar Basnet
In this article, we introduce a new graph theoretic structure associated with a finite commutative ring, called nil clean divisor graph. For a ring , nil clean divisor graph is…
Weak Nil Clean Ideal
Dhiren Kumar Basnet, Ajay Sharma
As a generalization of nil clean ideal, we define weak nil clean ideal of a ring. An ideal of a ring is weak nil clean ideal if for any , either or …
Nilpotent Graph
Dhiren Kumar Basnet, Ajay Sharma, Rahul Dutta
In this article, we introduce the concept of nilpotent graph of a finite commutative ring. The set of all non nilpotent elements of a ring is taken as the vertex set and two vertic…
Commuting probabilities of -centralizer finite rings
Jutirekha Dutta, Dhiren Kumar Basnet, Rajat Kanti Nath
Let be a finite ring. The commuting probability of , denoted by , is the probability that any two randomly chosen elements of commute. is called an -centr…