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- Title
On the crosscap of the annihilating-ideal graph of a commutative ring.
- Authors
Selvakumar, K.; Subbulakshmi, P.
- Abstract
Let R be a non-domain commutative ring with identity and A*(R) be the set of non-zero ideals with non-zero annihilators. We call an ideal I1 of R, an annihilating-ideal if there exists a non-zero ideal I2 of R such that I1I2 = (0). The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A*(R) and two distinct vertices I1 and I2 are adjacent if and only if I1I2 = (0). In this paper, we characterize all commutative Artinian non-local rings R for which AG(R) is planar and the crosscap of AG(R) is one.
- Subjects
COMMUTATIVE rings; GRAPH theory; SET theory
- Publication
Palestine Journal of Mathematics, 2018, Vol 7, Issue 1, p151
- ISSN
2219-5688
- Publication type
Article