The regular part of a semigroup of linear transformations with restricted range
© 2017 Australian Mathematical Publishing Association Inc. Let V be a vector space and let T(V) denote the semigroup (under composition) of all linear transformations from V into V. For a fixed subspace W of V, let T(V;W) be the semigroup consisting of all linear transformations from V into W. In 20...
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th-cmuir.6653943832-469922018-04-25T07:34:54Z The regular part of a semigroup of linear transformations with restricted range Worachead Sommanee Kritsada Sangkhanan Agricultural and Biological Sciences Arts and Humanities © 2017 Australian Mathematical Publishing Association Inc. Let V be a vector space and let T(V) denote the semigroup (under composition) of all linear transformations from V into V. For a fixed subspace W of V, let T(V;W) be the semigroup consisting of all linear transformations from V into W. In 2008, Sullivan ['Semigroups of linear transformations with restricted range', Bull. Aust. Math. Soc. 77(3) (2008), 441-453] proved that Q = {α ϵ T(V;W) : Vα ⊆ Wα} is the largest regular subsemigroup of T(V;W) and characterized Green's relations on T(V;W). In this paper, we determine all the maximal regular subsemigroups of Q whenW is a finite-dimensional subspace of V over a finite field. Moreover, we compute the rank and idempotent rank of Q when W is an ndimensional subspace of an m-dimensional vector space V over a finite field F. 2018-04-25T07:08:16Z 2018-04-25T07:08:16Z 2017-12-01 Journal 14468107 14467887 2-s2.0-85013080224 10.1017/S144678871600080X https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85013080224&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/46992 |
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Agricultural and Biological Sciences Arts and Humanities Worachead Sommanee Kritsada Sangkhanan The regular part of a semigroup of linear transformations with restricted range |
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© 2017 Australian Mathematical Publishing Association Inc. Let V be a vector space and let T(V) denote the semigroup (under composition) of all linear transformations from V into V. For a fixed subspace W of V, let T(V;W) be the semigroup consisting of all linear transformations from V into W. In 2008, Sullivan ['Semigroups of linear transformations with restricted range', Bull. Aust. Math. Soc. 77(3) (2008), 441-453] proved that Q = {α ϵ T(V;W) : Vα ⊆ Wα} is the largest regular subsemigroup of T(V;W) and characterized Green's relations on T(V;W). In this paper, we determine all the maximal regular subsemigroups of Q whenW is a finite-dimensional subspace of V over a finite field. Moreover, we compute the rank and idempotent rank of Q when W is an ndimensional subspace of an m-dimensional vector space V over a finite field F. |
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Worachead Sommanee Kritsada Sangkhanan |
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Worachead Sommanee Kritsada Sangkhanan |
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Worachead Sommanee |
title |
The regular part of a semigroup of linear transformations with restricted range |
title_short |
The regular part of a semigroup of linear transformations with restricted range |
title_full |
The regular part of a semigroup of linear transformations with restricted range |
title_fullStr |
The regular part of a semigroup of linear transformations with restricted range |
title_full_unstemmed |
The regular part of a semigroup of linear transformations with restricted range |
title_sort |
regular part of a semigroup of linear transformations with restricted range |
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2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85013080224&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/46992 |
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