SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET

Title & Authors
SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET
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) = {$\small{{\alpha}\;{\in}\;T(X)\;:\;Y\;{\alpha}\;{\subseteq}\;Y}$}. 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($\small{A^1}$, 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
1.
On certain order-preserving transformation semigroups, Communications in Algebra, 2017, 45, 7, 2980
2.
Semigroups of transformations with fixed sets, Quaestiones Mathematicae, 2013, 36, 1, 79
3.
REGULARITY OF TRANSFORMATION SEMIGROUPS DEFINED BY A PARTITION, Communications of the Korean Mathematical Society, 2016, 31, 2, 217
4.
NATURAL PARTIAL ORDER IN SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET, Bulletin of the Australian Mathematical Society, 2013, 87, 01, 94
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