Sub-semigroups determined by the zero-divisor graph

Details Sub-semigroups determined by the zero-divisor graph Sub-semigroups determined by the zero-divisor graph

2005-12-26

arxiv.org/abs/math/0512568v1

Mathematics

Rings and Algebras

14 pages

Scientific paper

In this paper we study sub-semigroups of a zero-divisor semigroup $S$ determined by properties of the zero-divisor graph $\Gamma(S)$. We use these sub-semigroups to study the correspondence between zero- divisor semigroups and zero-divisor graphs. We study properties of sub- semigroups of Boolean semigroups via the zero-divisor graph. As an application, we provide a characterization of the graphs which are zero- divisor graphs of Boolean rings.

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