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

1.

2.

References

1.

A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I and II, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I. 1961 and 1967.

2.

C. G. Doss, Certain equivalence relations in transformation semigroups, M. A. Thesis, directed by D. D. Miller, University of Tennessee, 1955.

3.

J. M. Howie, Fundamentals of Semigroup Theory, The Clarendon Press, Oxford University Press, New York, 1995.

4.

K. D. Magill Jr., Subsemigroups of S(X), Math. Japon. 11 (1966), 109-115.

5.

A. I. Malcev, Symmetric groupoids, Mat. Sbornik N. S. 31(73) (1952), 136-151.

6.

S. Nenthein, P. Youngkhong, and Y. Kemprasit, Regular elements of some transformation semigroups, Pure Math. Appl. 16 (2005), no. 3, 307-314.