A Note on a graph associated to a commutative ring
Publish place: The Journal of Algebra and Related Topics، Vol: 5، Issue: 1
Publish Year: 1396
نوع سند: مقاله ژورنالی
زبان: English
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JR_JART-5-1_006
تاریخ نمایه سازی: 31 تیر 1403
Abstract:
The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings. In this article, with any ring R, we associate an undirected graph denoted by G(R), whose vertex set is the set of all elements of R and distinct vertices x,y are joined by an edge in G(R) if and only if Rx\cap Ry = Rxy. In Section ۲ of this article, we classify rings R such that G(R) is complete and we also consider the problem of determining rings R such that \chi(G(R)) = \omega(G(R))< \infty. In Section ۳ of this article, we classify rings R such that G(R) is planar.
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Authors
S. Visweswaran
Saurashtra University
J. Parejiya
Saurashtra University