On semigroups of endomorphisms of a chain with restricted range
© 2013, Springer Science+Business Media New York. Let X be a finite or infinite chain and let ${\mathcal{O}}(X)$ be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of ${\mathcal{O}}(X)$ and Green’s relations on ${\mathcal{O}}(X)$. In fact, more gener...
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th-cmuir.6653943832-450022018-01-24T06:04:01Z On semigroups of endomorphisms of a chain with restricted range Vítor H. Fernandes Preeyanuch Honyam Teresa M. Quinteiro Boorapa Singha © 2013, Springer Science+Business Media New York. Let X be a finite or infinite chain and let ${\mathcal{O}}(X)$ be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of ${\mathcal{O}}(X)$ and Green’s relations on ${\mathcal{O}}(X)$. In fact, more generally, if Y is a nonempty subset of X and ${\mathcal{O}}(X,Y)$ is the subsemigroup of ${\mathcal{O}}(X)$ of all elements with range contained in Y, we characterize the largest regular subsemigroup of ${\mathcal{O}}(X,Y)$ and Green’s relations on ${\mathcal{O}}(X,Y)$. Moreover, for finite chains, we determine when two semigroups of the type ${\mathcal {O}}(X,Y)$ are isomorphic and calculate their ranks. 2018-01-24T06:04:01Z 2018-01-24T06:04:01Z 2014-08-01 Journal 00371912 2-s2.0-84942193328 10.1007/s00233-013-9548-x https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942193328&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/45002 |
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© 2013, Springer Science+Business Media New York. Let X be a finite or infinite chain and let ${\mathcal{O}}(X)$ be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of ${\mathcal{O}}(X)$ and Green’s relations on ${\mathcal{O}}(X)$. In fact, more generally, if Y is a nonempty subset of X and ${\mathcal{O}}(X,Y)$ is the subsemigroup of ${\mathcal{O}}(X)$ of all elements with range contained in Y, we characterize the largest regular subsemigroup of ${\mathcal{O}}(X,Y)$ and Green’s relations on ${\mathcal{O}}(X,Y)$. Moreover, for finite chains, we determine when two semigroups of the type ${\mathcal {O}}(X,Y)$ are isomorphic and calculate their ranks. |
| format |
Journal |
| author |
Vítor H. Fernandes Preeyanuch Honyam Teresa M. Quinteiro Boorapa Singha |
| spellingShingle |
Vítor H. Fernandes Preeyanuch Honyam Teresa M. Quinteiro Boorapa Singha On semigroups of endomorphisms of a chain with restricted range |
| author_facet |
Vítor H. Fernandes Preeyanuch Honyam Teresa M. Quinteiro Boorapa Singha |
| author_sort |
Vítor H. Fernandes |
| title |
On semigroups of endomorphisms of a chain with restricted range |
| title_short |
On semigroups of endomorphisms of a chain with restricted range |
| title_full |
On semigroups of endomorphisms of a chain with restricted range |
| title_fullStr |
On semigroups of endomorphisms of a chain with restricted range |
| title_full_unstemmed |
On semigroups of endomorphisms of a chain with restricted range |
| title_sort |
on semigroups of endomorphisms of a chain with restricted range |
| publishDate |
2018 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942193328&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/45002 |
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1681422664374157312 |