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- Title
Some properties of the essential annihilating-ideal graph of commutative rings.
- Authors
Nazim, Mohd; ur Rehman, Nadeem; Mir, Shabir Ahmad
- Abstract
Let S be a commutative ring with unity and A(S) denotes the set of annihilating-ideals of S. The essential annihilating-ideal graph of S, denoted by EG(S), is an undirected graph with A-(S) as the set of vertices and for distinct I;J 2 A-(S), I - J is an edge if and only if Ann(IJ) e S. In this paper, we classify the Artinian rings S for which EG(S) is projective. We also discuss the coloring of EG(S). Moreover, we discuss the domination number of EG(S).
- Subjects
COMMUTATIVE rings; RING theory; MATHEMATICAL constants; MATHEMATICS theorems; RATIONAL numbers; INTEGERS
- Publication
Communications in Combinatorics & Optimization, 2023, Vol 8, Issue 4, p715
- ISSN
2538-2128
- Publication type
Article
- DOI
10.22049/CCO.2022.27827.1365