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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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2018
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| Online Access: | 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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| Institution: | Chiang Mai University |
| Summary: | 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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