A topological property of a hypergraph assigned to commutative rings

Abstract

Studying algebraic structures via graphs and hypergraphs assigned to them can be of interest. Especially, computing the genus of a graph as a topological index leads to a better understanding of the related algebraic structure. In this direction we apply a hypergraph, namely [Formula: see text]-zero divisor hypergraph assigned to a commutative ring and study its genus. In this paper, we characterize all finite commutative nonlocal rings [Formula: see text] with identity whose [Formula: see text] has genus two. Further, we classify all finite commutative nonlocal rings [Formula: see text] whose [Formula: see text] has crosscap two. Moreover, we provide a MATLAB code for calculating [Formula: see text]-zero-divisor of [Formula: see text] and the hyperedge of [Formula: see text]-zero-divisor hypergraph of [Formula: see text].