Atul Gaur
University of Delhi
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Publication
Featured researches published by Atul Gaur.
Journal of Algebra and Its Applications | 2017
Rahul Kumar; Atul Gaur
Let R,T be commutative rings with identity such that R ⊆ T. We recall that R ⊆ T is called a λ-extension of rings if the set of all subrings of T containing R (the “intermediate rings”) is linearly ordered under inclusion. In this paper, a characterization of integrally closed λ-extension of rings is given. For example, we show that if R is a local ring, then R ⊆ T is an integrally closed λ-extension of rings if and only if there exists 𝔮 ∈Spec(R) such that T = R𝔮, 𝔮 = T𝔮 and R/𝔮 is a valuation domain. Let R be a subring of T such that R is invariant under action by G, where G is a subgroup of the automorphism group of T. If R ⊆ T is a λ-extension of rings, then RG ⊆ TG is a λ-extension of rings under some conditions.
Journal of Algebra and Its Applications | 2018
Rahul Kumar; Atul Gaur
Let R,T be commutative rings with identity such that R ⊆ T. A ring extension R ⊆ T is called a Δ-extension of rings if R1 + R2 is a subring of T for each pair of subrings R1,R2 of T containing R. I...
Discrete Mathematics, Algorithms and Applications | 2018
Arti Sharma; Atul Gaur
Let R be a commutative ring with nonzero identity. Let Γ(R) denote the maximal graph associated to R, that is, Γ(R) is a graph with vertices as non-units of R, where two distinct vertices a and b a...
Electronic Notes in Discrete Mathematics | 2017
Mukti Acharya; Pranjali; Atul Gaur; Amit Kumar
Abstract A signed total graph is an ordered pair T Σ ( Γ ( R ) ) : = ( T ( Γ ( R ) ) , σ ) , where T ( Γ ( R ) ) is the total graph of a commutative ring R, called the underlying graph of T Σ ( Γ ( R ) ) and T Σ ( Γ ( R ) ) is associated with a signing of its edges (a, b) by the function σ such that σ ( a , b ) is ‘+’ if a ∈ Z ( R ) or b ∈ Z ( R ) and ‘−’ otherwise. The aim of this paper is to gain a deeper insight into the notion of signed total graph by characterizing the rings for which line signed graph L ( T Σ ( Γ ( R ) ) ) of signed total graph are C-consistent, T Σ ( Γ ( R ) ) -consistent and sign-compatible.
Discrete Mathematics, Algorithms and Applications | 2016
Pranjali; Atul Gaur; Mukti Acharya
Motivated by the earlier study on the notion of signed total graph of a commutative ring, in this paper, we characterize all the commutative rings with unity for which signed total graph is 𝒞-consi...
International Journal of Algebra | 2007
Atul Gaur; Alok Kumar Maloo; Anand Parkash
International Journal of Algebra | 2013
Atul Gaur; Arti Sharma
Archive | 2008
Atul Gaur; Alok Kumar Maloo
Indian Journal of Pure & Applied Mathematics | 2017
Atul Gaur; Arti Sharma
Journal of Algebra and Related Topics | 2015
Arti Sharma; Atul Gaur