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- Title
Sum Ideal Graphs Associated to a Given Ideal of a Commutative Ring.
- Authors
Nadir, A. H.; Abdulqadr, F. H.; Shuker, N. H.
- Abstract
The aim of this paper is to introduce and study a new kind of graphs associated to an ideal of a commutative ring. Let R be a commutative ring with identity, and I(R) be the set of all non-trivial ideals of R with S∈I(R). The sum ideal graph associated to S, denoted by Ψ(R, S), is the undirected graph with vertex set {A∈I(R): S⊂A+B, for some B∈I(R)} where two ideal vertices A and B are adjacent if and only if A B and S⊂A+B. In this paper we establish some of characterizations and results of this kind of graph with providing some examples.
- Subjects
CHARTS, diagrams, etc.; GRAPHIC methods; COMMUTATIVE rings; COMMUTATIVE algebra; MAXIMAL ideals
- Publication
Iraqi Journal of Science, 2019, Vol 60, Issue 11, p2478
- ISSN
0067-2904
- Publication type
Article
- DOI
10.24996/ijs.2019.60.11.19