Glasnik Matematicki, Vol. 43, No.2 (2008), 309-320.

THE ZERO-DIVISOR GRAPH WITH RESPECT TO IDEALS OF A COMMUTATIVE SEMIRING

Shahabaddin Ebrahimi Atani

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

Abstract.   In a manner analogous to a commutative ring, the ideal-based zero-divisor graph of a commutative semiring R can be defined as the undirected graph ΓI(R) for some ideal I of R. The properties and possible structures of the graph ΓI(R) are studied.

2000 Mathematics Subject Classification.   16Y60, 05C75.

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

Full text (PDF) (free access)

DOI: 10.3336/gm.43.2.06

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