Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals
© 2015, Springer Basel. Let X be a chain and OT(X) the full order-preserving transformation semigroup on X. Let Y be a fixed nonempty subset of X and let OT(X, Y) be the subsemigroup of OT(X) of all order-preserving transformations with ranges contained in Y. In this paper, we investigate the order-...
Saved in:
Main Authors: | , |
---|---|
Format: | Journal |
Published: |
2018
|
Subjects: | |
Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942191518&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/44061 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Chiang Mai University |
id |
th-cmuir.6653943832-44061 |
---|---|
record_format |
dspace |
spelling |
th-cmuir.6653943832-440612018-04-25T07:45:13Z Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals Worachead Sommanee Jintana Sanwong Agricultural and Biological Sciences © 2015, Springer Basel. Let X be a chain and OT(X) the full order-preserving transformation semigroup on X. Let Y be a fixed nonempty subset of X and let OT(X, Y) be the subsemigroup of OT(X) of all order-preserving transformations with ranges contained in Y. In this paper, we investigate the order-preserving transformation semigroupOF(X,Y)={α∈OT(X,Y):Xα=Yα}.Here, we characterize when an element of OF(X, Y) is regular and describe Green’s relations in OF(X, Y). Moreover, we give a simpler description of Green’s relations, characterize the ideals of OF(X, Y) when Y is a finite subset of X, and apply these results to prove that OF(X, Y) is idempotent generated. 2018-01-24T04:37:38Z 2018-01-24T04:37:38Z 2015-11-25 Journal 00025240 2-s2.0-84942191518 10.1007/s00012-015-0354-z https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942191518&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/44061 |
institution |
Chiang Mai University |
building |
Chiang Mai University Library |
country |
Thailand |
collection |
CMU Intellectual Repository |
topic |
Agricultural and Biological Sciences |
spellingShingle |
Agricultural and Biological Sciences Worachead Sommanee Jintana Sanwong Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals |
description |
© 2015, Springer Basel. Let X be a chain and OT(X) the full order-preserving transformation semigroup on X. Let Y be a fixed nonempty subset of X and let OT(X, Y) be the subsemigroup of OT(X) of all order-preserving transformations with ranges contained in Y. In this paper, we investigate the order-preserving transformation semigroupOF(X,Y)={α∈OT(X,Y):Xα=Yα}.Here, we characterize when an element of OF(X, Y) is regular and describe Green’s relations in OF(X, Y). Moreover, we give a simpler description of Green’s relations, characterize the ideals of OF(X, Y) when Y is a finite subset of X, and apply these results to prove that OF(X, Y) is idempotent generated. |
format |
Journal |
author |
Worachead Sommanee Jintana Sanwong |
author_facet |
Worachead Sommanee Jintana Sanwong |
author_sort |
Worachead Sommanee |
title |
Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals |
title_short |
Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals |
title_full |
Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals |
title_fullStr |
Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals |
title_full_unstemmed |
Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals |
title_sort |
order-preserving transformations with restricted range: regularity, green’s relations, and ideals |
publishDate |
2018 |
url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942191518&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/44061 |
_version_ |
1681422489477971968 |