Glasnik matematički, Vol. 44 No. 1, 2009.
Original scientific paper
https://doi.org/10.3336/gm.44.1.07
An ideal based zero-divisor graph of a commutative semiring
Shahabaddin Ebrahimi Atani
; Department of Mathematics, University of Guilan, 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.
Keywords
Semiring; zero-divisor; graph; primal; ideal-based
Hrčak ID:
36948
URI
Publication date:
21.5.2009.
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