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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| 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=84896301309&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/45351 |
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| Institution: | Chiang Mai University |
| Summary: | 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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