| Autor: |
Visweswaran, S. |
| Předmět: |
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| Zdroj: |
Discrete Mathematics, Algorithms & Applications; Oct2024, Vol. 16 Issue 7, p1-34, 34p |
| Abstrakt: |
The rings considered in this paper are commutative with identity which are not integral domains. Let R be a ring. An ideal I of R is said to be an annihilating ideal if there exists r ∈ R \ { 0 } such that I r = (0). Let (R) denote the set of all annihilating ideals of R and we denote (R) \ { (0) } by (R) ∗ . With R , in this paper, we associate an undirected graph denoted by S Ω (R) whose vertex set is (R) ∗ and two distinct vertices I , J are adjacent in this graph if and only if either I J = (0) or I + J ∈ (R). The aim of this paper is to study the interplay between some graph properties of S Ω (R) and the algebraic properties of R and to compare some graph properties of S Ω (R) with the corresponding graph properties of the annihilating ideal graph of R and the sum annihilating ideal graph of R. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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