Semigroups of injective partial linear transformations with restricted range: Green's relations and partial orders
Let V be any vector space and I(V) the set of all partial injective linear transformations defined on V, that is, all injective linear transformations α: A → B where A, B are subspaces of V. Then I(V) is a semigroup under composition. Let W be a subspace of V. Define I(V, W)={α∈ I(V): V α ⊆ W}. So I...
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th-cmuir.6653943832-517792018-09-04T06:08:53Z Semigroups of injective partial linear transformations with restricted range: Green's relations and partial orders Kritsada Sangkhanan Jintana Sanwong Mathematics Let V be any vector space and I(V) the set of all partial injective linear transformations defined on V, that is, all injective linear transformations α: A → B where A, B are subspaces of V. Then I(V) is a semigroup under composition. Let W be a subspace of V. Define I(V, W)={α∈ I(V): V α ⊆ W}. So I(V,W) is a subsemigroup of I(V). In this paper, we present the largest regular subsemigroup of I(V, W) and determine its Green's relations. Furthermore, we study the natural partial order ≤ on I(V, W) in terms of domains and images, compare ≤ with the subset order and find elements of I(V, W) which are compatible. © 2012 Academic Publications, Ltd. 2018-09-04T06:08:53Z 2018-09-04T06:08:53Z 2012-11-19 Journal 13143395 13118080 2-s2.0-84869017393 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84869017393&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51779 |
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Mathematics Kritsada Sangkhanan Jintana Sanwong Semigroups of injective partial linear transformations with restricted range: Green's relations and partial orders |
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Let V be any vector space and I(V) the set of all partial injective linear transformations defined on V, that is, all injective linear transformations α: A → B where A, B are subspaces of V. Then I(V) is a semigroup under composition. Let W be a subspace of V. Define I(V, W)={α∈ I(V): V α ⊆ W}. So I(V,W) is a subsemigroup of I(V). In this paper, we present the largest regular subsemigroup of I(V, W) and determine its Green's relations. Furthermore, we study the natural partial order ≤ on I(V, W) in terms of domains and images, compare ≤ with the subset order and find elements of I(V, W) which are compatible. © 2012 Academic Publications, Ltd. |
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Journal |
| author |
Kritsada Sangkhanan Jintana Sanwong |
| author_facet |
Kritsada Sangkhanan Jintana Sanwong |
| author_sort |
Kritsada Sangkhanan |
| title |
Semigroups of injective partial linear transformations with restricted range: Green's relations and partial orders |
| title_short |
Semigroups of injective partial linear transformations with restricted range: Green's relations and partial orders |
| title_full |
Semigroups of injective partial linear transformations with restricted range: Green's relations and partial orders |
| title_fullStr |
Semigroups of injective partial linear transformations with restricted range: Green's relations and partial orders |
| title_full_unstemmed |
Semigroups of injective partial linear transformations with restricted range: Green's relations and partial orders |
| title_sort |
semigroups of injective partial linear transformations with restricted range: green's relations and partial orders |
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2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84869017393&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51779 |
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