On the genus of annihilator intersection graph of commutative rings

Document Type : Research Paper

Authors

1 Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.

2 Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-627012, India.

Abstract

Let R be a commutative ring with unity and A(R) be the set of annihilating-ideals of R. The annihilator intersection graph of R, represented by AIG(R), is an undirected graph with A(R)∗ as the vertex set and M∼N is an edge of AIG(R) if and only if Ann(MN)≠Ann(M)∩Ann(N), for distinct vertices M and N of AIG(R). In this paper, we first defined finite commutative rings whose annihilator intersection graph is isomorphic to various well-known graphs, and then all finite commutative rings with a planar or toroidal annihilator intersection graph were characterized.

Keywords

References

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Algebraic Structures and Their Applications
Volume 11, Issue 1
February 2024
Pages 25-36

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