Injective partial transformations with infinite defects

In 2003, Marques-Smith and Sullivan described the join Ω of the 'natural order' ≤ and the 'containment order' ⊆ on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial B...

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Main Authors: Boorapa Singha, Jintana Sanwong, Robert Patrick Sullivan
Format: Journal
Published: 2018
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Online Access:http://dx.doi.org/10.4134/BKMS.2012.49.1.109
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-518082018-09-04T06:09:30Z Injective partial transformations with infinite defects Boorapa Singha Jintana Sanwong Robert Patrick Sullivan Mathematics In 2003, Marques-Smith and Sullivan described the join Ω of the 'natural order' ≤ and the 'containment order' ⊆ on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial Baer-Levi semigroup consisting of all injective α {small element of} P(X) such that {pipe}X \ Xα{pipe} = q, where א 0 ≤ q ≤ {pipe}X{pipe}. In this paper, we describe the group of automorphisms of R(q), the largest regular subsemigroup of PS(q). In 2010, we studied some properties of ≤ and ⊆ on PS(q). Here, we characterize the meet and join under those orders for elements of R(q) and PS(q). In addition, since ≤ does not equal Ω on I(X), the symmetric inverse semigroup on X, we formulate an algebraic version of Ω on arbitrary inverse semigroups and discuss some of its properties in an algebraic setting. © 2012 The Korean Mathematical Society. 2018-09-04T06:09:30Z 2018-09-04T06:09:30Z 2012-02-20 Journal 10158634 2-s2.0-84856818878 http://dx.doi.org/10.4134/BKMS.2012.49.1.109 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84856818878&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51808
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Boorapa Singha
Jintana Sanwong
Robert Patrick Sullivan
Injective partial transformations with infinite defects
description In 2003, Marques-Smith and Sullivan described the join Ω of the 'natural order' ≤ and the 'containment order' ⊆ on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial Baer-Levi semigroup consisting of all injective α {small element of} P(X) such that {pipe}X \ Xα{pipe} = q, where א 0 ≤ q ≤ {pipe}X{pipe}. In this paper, we describe the group of automorphisms of R(q), the largest regular subsemigroup of PS(q). In 2010, we studied some properties of ≤ and ⊆ on PS(q). Here, we characterize the meet and join under those orders for elements of R(q) and PS(q). In addition, since ≤ does not equal Ω on I(X), the symmetric inverse semigroup on X, we formulate an algebraic version of Ω on arbitrary inverse semigroups and discuss some of its properties in an algebraic setting. © 2012 The Korean Mathematical Society.
format Journal
author Boorapa Singha
Jintana Sanwong
Robert Patrick Sullivan
author_facet Boorapa Singha
Jintana Sanwong
Robert Patrick Sullivan
author_sort Boorapa Singha
title Injective partial transformations with infinite defects
title_short Injective partial transformations with infinite defects
title_full Injective partial transformations with infinite defects
title_fullStr Injective partial transformations with infinite defects
title_full_unstemmed Injective partial transformations with infinite defects
title_sort injective partial transformations with infinite defects
publishDate 2018
url http://dx.doi.org/10.4134/BKMS.2012.49.1.109
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84856818878&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/51808
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