Green's relations and partial orders on semigroups of partial linear transformations with restricted range
Let V be any vector space and P(V) the set of all partial linear transformations defined on V, that is, all linear transformations α: S → T where S; T are subspaces of V. Then P(V) is a semigroup under composition. Let W be a subspace of V. We define PT(V;W) = {α ∈ P(V): Vα ⊆ W}. So PT(V,W) is a sub...
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th-cmuir.6653943832-536792018-09-04T09:55:15Z Green's relations and partial orders on semigroups of partial linear transformations with restricted range Kritsada Sangkhanan Jintana Sanwong Mathematics Let V be any vector space and P(V) the set of all partial linear transformations defined on V, that is, all linear transformations α: S → T where S; T are subspaces of V. Then P(V) is a semigroup under composition. Let W be a subspace of V. We define PT(V;W) = {α ∈ P(V): Vα ⊆ W}. So PT(V,W) is a subsemigroup of P(V). In this paper, we present the largest regular subsemigroup and determine Green's relations on PT(V;W). Furthermore, we study the natural partial order ≤ on PT(V;W) in terms of domains and images and find elements of PT(V,W) which are compatible. © 2014 by the Mathematical Association of Thailand. All rights reserved. 2018-09-04T09:55:15Z 2018-09-04T09:55:15Z 2014-01-01 Journal 16860209 2-s2.0-84896301309 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84896301309&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/53679 |
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Mathematics Kritsada Sangkhanan Jintana Sanwong Green's relations and partial orders on semigroups of partial linear transformations with restricted range |
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Let V be any vector space and P(V) the set of all partial linear transformations defined on V, that is, all linear transformations α: S → T where S; T are subspaces of V. Then P(V) is a semigroup under composition. Let W be a subspace of V. We define PT(V;W) = {α ∈ P(V): Vα ⊆ W}. So PT(V,W) is a subsemigroup of P(V). In this paper, we present the largest regular subsemigroup and determine Green's relations on PT(V;W). Furthermore, we study the natural partial order ≤ on PT(V;W) in terms of domains and images and find elements of PT(V,W) which are compatible. © 2014 by the Mathematical Association of Thailand. All rights reserved. |
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Journal |
| author |
Kritsada Sangkhanan Jintana Sanwong |
| author_facet |
Kritsada Sangkhanan Jintana Sanwong |
| author_sort |
Kritsada Sangkhanan |
| title |
Green's relations and partial orders on semigroups of partial linear transformations with restricted range |
| title_short |
Green's relations and partial orders on semigroups of partial linear transformations with restricted range |
| title_full |
Green's relations and partial orders on semigroups of partial linear transformations with restricted range |
| title_fullStr |
Green's relations and partial orders on semigroups of partial linear transformations with restricted range |
| title_full_unstemmed |
Green's relations and partial orders on semigroups of partial linear transformations with restricted range |
| title_sort |
green's relations and partial orders on semigroups of partial linear transformations with restricted range |
| publishDate |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84896301309&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/53679 |
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