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null semigroup
In mathematics, a null semigroup (also called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two elements is zero. If every element of the semigroup is a left zero then the semigroup is called a left zero semigroup; a right zero semigroup is defined analogously.〔M. Kilp, U. Knauer, A.V. Mikhalev, ''Monoids, Acts and Categories with Applications to Wreath Products and Graphs'', De Gruyter Expositions in Mathematics vol. 29, Walter de Gruyter, 2000, ISBN 3-11-015248-7, p. 19〕
According to Clifford and Preston, "In spite of their triviality, these semigroups arise naturally in a number of investigations."〔
==Null semigroup==
Let ''S'' be a semigroup with zero element 0. Then ''S'' is called a ''null semigroup'' if for all ''x'' and ''y'' in ''S'' we have ''xy'' = 0.
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