1. On two extensions of the annihilating-ideal graph of commutative rings.
- Author
-
Nazim, Mohd, Rehman, Nadeem ur, and Nisar, Junaid
- Subjects
- *
COMMUTATIVE rings , *UNDIRECTED graphs , *INTEGERS - Abstract
Let R be a commutative ring with A (R) its set of annihilating-ideals. The extended annihilating-ideal graph of R, denoted by AG ¯ (R) , is an undirected graph with vertex set A (R) * = A (R) ∖ { 0 } and two vertices I 1 and I 2 are adjacent if and only if I 1 m I 2 n = 0 with I 1 m ≠ 0 and I 2 n ≠ 0 , for some positive integers m and n. In this paper, we first study some basic properties of AG ¯ (R) and then we investigate the relationship between the extended annihilating-ideal graph AG ¯ (R) , the annihilator-ideal graph A I (R) and the annihilating-ideal graph AG (R) of a commutative ring R. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF