Regularity and Green's Relations on a Semigroup of Transformations with Restricted Range

Jintana Sanwong and Worachead Sommanee

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-11

Abstract:

Let be the full transformation semigroup on the set and let . Then is a sub-semigroup of determined by a nonempty subset of . In this paper, we give a necessary and sufficient condition for to be regular. In the case that is not regular, the largest regular sub-semigroup is obtained and this sub-semigroup is shown to determine the Green's relations on . Also, a class of maximal inverse sub-semigroups of is obtained.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:794013

DOI: 10.1155/2008/794013

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