NATURALLY ORDERED TRANSFORMATION SEMIGROUPS PRESERVING AN EQUIVALENCE-Reference-Cited by-同舟云学术

NATURALLY ORDERED TRANSFORMATION SEMIGROUPS PRESERVING AN EQUIVALENCE

Published:2008-08 Issue:1 Volume:78 Page:117-128
ISSN:0004-9727
Container-title:Bulletin of the Australian Mathematical Society
language:en
Short-container-title:Bull. Austral. Math. Soc.

Author:

SUN LEI,PEI HUISHENG,CHENG ZHENGXING

Abstract

AbstractLet 𝒯X be the full transformation semigroup on a set X and E be a nontrivial equivalence on X. Write then TE(X) is a subsemigroup of 𝒯X. In this paper, we endow TE(X) with the so-called natural order and determine when two elements of TE(X) are related under this order, then find out elements of TE(X) which are compatible with ≤ on TE(X). Also, the maximal and minimal elements and the covering elements are described.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference11 articles.

1. A natural partial order for semigroups

2. On the rank of the semigroup TE(X);Pei;Semigroup Forum,2005

3. Regularity and Green’s relations for semigroups of transformations that preserve an equivalence;Pei;Comm. Algebra,2005

4. Equivalences, α-semigroups and α-congruences;Pei;Semigroup Forum,1994

5. Green's Relations for the Variants of Transformation Semigroups Preserving an Equivalence Relation

Cited by 15 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Green’s relations on the variant semigroups of all transformations of a set that reflect an equivalence;Semigroup Forum;2024-06

2. The natural partial order on semigroups of transformations with restricted range that preserve an equivalence;Semigroup Forum;2024-03-27

3. Regularity and abundance on semigroups of transformations preserving an equivalence relation on an invariant set;AIMS Mathematics;2023

4. A partial order on transformation semigroups with restricted range that preserve double direction equivalence;Open Mathematics;2021-01-01

5. Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence;Semigroup Forum;2020-02-07