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...
Saved in:
Main Authors: | , |
---|---|
Format: | Journal |
Published: |
2018
|
Subjects: | |
Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85013080224&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57503 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Institution: | Chiang Mai University |
id |
th-cmuir.6653943832-57503 |
---|---|
record_format |
dspace |
spelling |
th-cmuir.6653943832-575032018-09-05T03:44:07Z The regular part of a semigroup of linear transformations with restricted range Worachead Sommanee Kritsada Sangkhanan Mathematics © 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. 2018-09-05T03:44:07Z 2018-09-05T03:44:07Z 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/6653943832/57503 |
institution |
Chiang Mai University |
building |
Chiang Mai University Library |
country |
Thailand |
collection |
CMU Intellectual Repository |
topic |
Mathematics |
spellingShingle |
Mathematics Worachead Sommanee Kritsada Sangkhanan The regular part of a semigroup of linear transformations with restricted range |
description |
© 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. |
format |
Journal |
author |
Worachead Sommanee Kritsada Sangkhanan |
author_facet |
Worachead Sommanee Kritsada Sangkhanan |
author_sort |
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 |
publishDate |
2018 |
url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85013080224&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57503 |
_version_ |
1681424890982301696 |