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: Vítor H. Fernandes, Jintana Sanwong
Format: Journal
Published: 2018
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84903307086&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/45628
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spelling th-cmuir.6653943832-456282018-01-24T06:14:03Z On the ranks of semigroups of transformations on a finite set with restricted range Vítor H. Fernandes Jintana Sanwong 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. 2018-01-24T06:14:03Z 2018-01-24T06:14:03Z 2014-01-01 Journal 10053867 2-s2.0-84903307086 10.1142/S1005386714000431 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84903307086&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/45628
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
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 Journal
author Vítor H. Fernandes
Jintana Sanwong
spellingShingle Vítor H. Fernandes
Jintana Sanwong
On the ranks of semigroups of transformations on a finite set with restricted range
author_facet Vítor H. Fernandes
Jintana Sanwong
author_sort Vítor H. Fernandes
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
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84903307086&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/45628
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