SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET

- Journal title : Journal of the Korean Mathematical Society
- Volume 48, Issue 2, 2011, pp.289-300
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2011.48.2.289

Title & Authors

SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET

Honyam, Preeyanuch; Sanwong, Jintana;

Honyam, Preeyanuch; Sanwong, Jintana;

Abstract

Let T(X) denote the semigroup (under composition) of transformations from X into itself. For a fixed nonempty subset Y of X, let S(X, Y) = {}. Then S(X, Y) is a semigroup of total transformations of X which leave a subset Y of X invariant. In this paper, we characterize when S(X, Y) is isomorphic to T(Z) for some set Z and prove that every semigroup A can be embedded in S(, A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals.

Keywords

transformation semigroups;Green's relations;ideals;

Language

English

Cited by

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