SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET

被引：26

作者：

Honyam, Preeyanuch ^{[1
]}

Sanwong, Jintana ^{[1
]}

机构：

[1] Chiang Mai Univ, Dept Math, Chiang Mai 50200, Thailand

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2011年 / 48卷 / 02期

关键词：

transformation semigroups; Green's relations; ideals;

D O I：

10.4134/JKMS.2011.48.2.289

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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) = {alpha is an element of T(X) : Y alpha subset of 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(1), A). Then we describe Green's relations for S(X, Y) and apply these results to obtain its group H-classes and ideals.

引用

页码：289 / 300

页数：12