On the ranks of semigroups of transformations on a finite set with restricted range

Let PT (X) be the semigroup of all partial transformations on X, T (X) and I(X) be the subsemigroups of PT (X) of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let PT (X; Y ) = {α ∈ PT (X) : Xα ⊆ Y}, T (X; Y ) = PT (X;...

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Main Authors: Fernandes V.H., Sanwong J.
Format: Article
Language:English
Published: World Scientific Publishing Co. Pte Ltd 2014
Online Access:http://www.scopus.com/inward/record.url?eid=2-s2.0-84903307086&partnerID=40&md5=ee331bd7f2c26a2532d9d6dfad19e759
http://cmuir.cmu.ac.th/handle/6653943832/4876
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spelling th-cmuir.6653943832-48762014-08-30T02:55:54Z On the ranks of semigroups of transformations on a finite set with restricted range Fernandes V.H. Sanwong J. Let PT (X) be the semigroup of all partial transformations on X, T (X) and I(X) be the subsemigroups of PT (X) of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let PT (X; Y ) = {α ∈ PT (X) : Xα ⊆ Y}, T (X; Y ) = PT (X; Y ) \ T (X) and I(X; Y ) = PT (X; Y ) \ I(X). In 2008, Sanwong and Sommanee described the largest regular subsemigroup and determined Green's relations of T (X; Y ). In this paper, we present analogous results for both PT (X; Y ) and I(X; Y ). For a finite set X with jXj - 3, the ranks of PT (X) = PT (X;X), T (X) = T (X;X) and I(X) = I(X;X) are well known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of PT (X; Y ), T (X; Y ) and I(X; Y ) for any proper non-empty subset Y of X. © 2014 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University. 2014-08-30T02:55:54Z 2014-08-30T02:55:54Z 2014 Article 10053867 10.1142/S1005386714000431 http://www.scopus.com/inward/record.url?eid=2-s2.0-84903307086&partnerID=40&md5=ee331bd7f2c26a2532d9d6dfad19e759 http://cmuir.cmu.ac.th/handle/6653943832/4876 English World Scientific Publishing Co. Pte Ltd
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
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language English
description Let PT (X) be the semigroup of all partial transformations on X, T (X) and I(X) be the subsemigroups of PT (X) of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let PT (X; Y ) = {α ∈ PT (X) : Xα ⊆ Y}, T (X; Y ) = PT (X; Y ) \ T (X) and I(X; Y ) = PT (X; Y ) \ I(X). In 2008, Sanwong and Sommanee described the largest regular subsemigroup and determined Green's relations of T (X; Y ). In this paper, we present analogous results for both PT (X; Y ) and I(X; Y ). For a finite set X with jXj - 3, the ranks of PT (X) = PT (X;X), T (X) = T (X;X) and I(X) = I(X;X) are well known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of PT (X; Y ), T (X; Y ) and I(X; Y ) for any proper non-empty subset Y of X. © 2014 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.
format Article
author Fernandes V.H.
Sanwong J.
spellingShingle Fernandes V.H.
Sanwong J.
On the ranks of semigroups of transformations on a finite set with restricted range
author_facet Fernandes V.H.
Sanwong J.
author_sort Fernandes V.H.
title On the ranks of semigroups of transformations on a finite set with restricted range
title_short On the ranks of semigroups of transformations on a finite set with restricted range
title_full On the ranks of semigroups of transformations on a finite set with restricted range
title_fullStr On the ranks of semigroups of transformations on a finite set with restricted range
title_full_unstemmed On the ranks of semigroups of transformations on a finite set with restricted range
title_sort on the ranks of semigroups of transformations on a finite set with restricted range
publisher World Scientific Publishing Co. Pte Ltd
publishDate 2014
url http://www.scopus.com/inward/record.url?eid=2-s2.0-84903307086&partnerID=40&md5=ee331bd7f2c26a2532d9d6dfad19e759
http://cmuir.cmu.ac.th/handle/6653943832/4876
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