Glasnik Matematicki, Vol. 44, No.1 (2009), 141-153.

AN IDEAL-BASED ZERO-DIVISOR GRAPH OF A COMMUTATIVE SEMIRING

Shahabaddin Ebrahimi Atani

Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran

Abstract.   There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of ΓI(R) for some ideal I of R. We also show that the zero-divisor graph with respect to primal ideals commutes by the semiring of fractions of R.

2000 Mathematics Subject Classification.   16Y60, 05C75.

Key words and phrases.   Semiring, zero-divisor, graph, primal, ideal-based.

Full text (PDF) (free access)

DOI: 10.3336/gm.44.1.07

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