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-...
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th-cmuir.6653943832-546432018-09-04T10:19:12Z Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals Worachead Sommanee Jintana Sanwong Mathematics © 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. 2018-09-04T10:19:12Z 2018-09-04T10:19:12Z 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/6653943832/54643 |
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Mathematics |
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Mathematics Worachead Sommanee Jintana Sanwong Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals |
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© 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 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942191518&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/54643 |
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