Partial orders on semigroups of partial transformations with restricted range
Let X be any set and P(X) the set of all partial transformations defined on X, that is, all functions α:A→B where A,B are subsets of X. Then P(X) is a semigroup under composition. Let Y be a subset of X. Recently, Fernandes and Sanwong defined PT(X,Y)={α P(X):XαY } and defined I(X,Y) to be the set o...
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th-cmuir.6653943832-517942018-09-04T06:09:11Z Partial orders on semigroups of partial transformations with restricted range Kritsada Sangkhanan Jintana Sanwong Mathematics Let X be any set and P(X) the set of all partial transformations defined on X, that is, all functions α:A→B where A,B are subsets of X. Then P(X) is a semigroup under composition. Let Y be a subset of X. Recently, Fernandes and Sanwong defined PT(X,Y)={α P(X):XαY } and defined I(X,Y) to be the set of all injective transformations in PT(X,Y). Hence PT(X,Y) and I(X,Y) are subsemigroups of P(X). In this paper, we study properties of the so-called natural partial order ≥ on PT(X,Y) and I(X,Y) in terms of domains, images and kernels, compare ≥ with the subset order, characterise the meet and join of these two orders, then find elements of PT(X,Y) and I(X,Y) which are compatible. Also, the minimal and maximal elements are described. © 2012 Australian Mathematical Publishing Association Inc. 2018-09-04T06:09:11Z 2018-09-04T06:09:11Z 2012-08-01 Journal 17551633 00049727 2-s2.0-84864870168 10.1017/S0004972712000020 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84864870168&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51794 |
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Mathematics Kritsada Sangkhanan Jintana Sanwong Partial orders on semigroups of partial transformations with restricted range |
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Let X be any set and P(X) the set of all partial transformations defined on X, that is, all functions α:A→B where A,B are subsets of X. Then P(X) is a semigroup under composition. Let Y be a subset of X. Recently, Fernandes and Sanwong defined PT(X,Y)={α P(X):XαY } and defined I(X,Y) to be the set of all injective transformations in PT(X,Y). Hence PT(X,Y) and I(X,Y) are subsemigroups of P(X). In this paper, we study properties of the so-called natural partial order ≥ on PT(X,Y) and I(X,Y) in terms of domains, images and kernels, compare ≥ with the subset order, characterise the meet and join of these two orders, then find elements of PT(X,Y) and I(X,Y) which are compatible. Also, the minimal and maximal elements are described. © 2012 Australian Mathematical Publishing Association Inc. |
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Journal |
| author |
Kritsada Sangkhanan Jintana Sanwong |
| author_facet |
Kritsada Sangkhanan Jintana Sanwong |
| author_sort |
Kritsada Sangkhanan |
| title |
Partial orders on semigroups of partial transformations with restricted range |
| title_short |
Partial orders on semigroups of partial transformations with restricted range |
| title_full |
Partial orders on semigroups of partial transformations with restricted range |
| title_fullStr |
Partial orders on semigroups of partial transformations with restricted range |
| title_full_unstemmed |
Partial orders on semigroups of partial transformations with restricted range |
| title_sort |
partial orders on semigroups of partial transformations with restricted range |
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2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84864870168&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51794 |
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