Ranks and isomorphism theorems of semigroups of linear transformations with restricted range

© 2018 Springer Science+Business Media, LLC, part of Springer Nature Let P(V) be the partial linear transformation semigroup of a vector space V under composition. Given a fixed subspace W of V, define the following subsemigroups of P(V): (Formula presented.)In this paper, we prove certain isomorphi...

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Main Authors:	Kritsada Sangkhanan, Jintana Sanwong
Format:	Journal
Published:	2018
Subjects:	Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85049951974&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58798
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Institution:	Chiang Mai University

id	th-cmuir.6653943832-58798
record_format	dspace
spelling	th-cmuir.6653943832-587982018-09-05T04:32:27Z Ranks and isomorphism theorems of semigroups of linear transformations with restricted range Kritsada Sangkhanan Jintana Sanwong Mathematics © 2018 Springer Science+Business Media, LLC, part of Springer Nature Let P(V) be the partial linear transformation semigroup of a vector space V under composition. Given a fixed subspace W of V, define the following subsemigroups of P(V): (Formula presented.)In this paper, we prove certain isomorphism theorems and compute the ranks of these three semigroups for any proper subspace W of V when V is a finite-dimensional vector space over a finite field. Gaussian binomial coefficients play an essential role in these computations. 2018-09-05T04:32:27Z 2018-09-05T04:32:27Z 2018-07-16 Journal 00371912 2-s2.0-85049951974 10.1007/s00233-018-9956-z https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85049951974&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58798
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics Kritsada Sangkhanan Jintana Sanwong Ranks and isomorphism theorems of semigroups of linear transformations with restricted range
description	© 2018 Springer Science+Business Media, LLC, part of Springer Nature Let P(V) be the partial linear transformation semigroup of a vector space V under composition. Given a fixed subspace W of V, define the following subsemigroups of P(V): (Formula presented.)In this paper, we prove certain isomorphism theorems and compute the ranks of these three semigroups for any proper subspace W of V when V is a finite-dimensional vector space over a finite field. Gaussian binomial coefficients play an essential role in these computations.
format	Journal
author	Kritsada Sangkhanan Jintana Sanwong
author_facet	Kritsada Sangkhanan Jintana Sanwong
author_sort	Kritsada Sangkhanan
title	Ranks and isomorphism theorems of semigroups of linear transformations with restricted range
title_short	Ranks and isomorphism theorems of semigroups of linear transformations with restricted range
title_full	Ranks and isomorphism theorems of semigroups of linear transformations with restricted range
title_fullStr	Ranks and isomorphism theorems of semigroups of linear transformations with restricted range
title_full_unstemmed	Ranks and isomorphism theorems of semigroups of linear transformations with restricted range
title_sort	ranks and isomorphism theorems of semigroups of linear transformations with restricted range
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85049951974&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58798
_version_	1681425132766101504

Ranks and isomorphism theorems of semigroups of linear transformations with restricted range

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