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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…
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…