Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions
© 2019 World Scientific Publishing Company Let (Formula presented.) be a vector space and (Formula presented.) denote the semigroup (under the composition of maps) of all linear transformations from (Formula presented.) into itself. For a fixed subspace (Formula presented.) of (Formula presented.),...
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th-cmuir.6653943832-588012018-09-05T04:32:39Z Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions Yanisa Chaiya Chollawat Pookpienlert Jintana Sanwong Mathematics © 2019 World Scientific Publishing Company Let (Formula presented.) be a vector space and (Formula presented.) denote the semigroup (under the composition of maps) of all linear transformations from (Formula presented.) into itself. For a fixed subspace (Formula presented.) of (Formula presented.), let (Formula presented.) be the subsemigroup of (Formula presented.) consisting of all linear transformations on (Formula presented.) which fix all elements in (Formula presented.). In this paper, we describe Green’s relations, regularity and ideals of (Formula presented.); and characterize when (Formula presented.) is factorizable, unit-regular and directly finite, from which the results on (Formula presented.) can be recaptured easily when taking (Formula presented.) as a zero subspace of (Formula presented.). 2018-09-05T04:32:39Z 2018-09-05T04:32:39Z 2018-06-04 Journal 17937183 17935571 2-s2.0-85047971291 10.1142/S1793557119500621 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85047971291&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58801 |
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Mathematics Yanisa Chaiya Chollawat Pookpienlert Jintana Sanwong Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions |
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© 2019 World Scientific Publishing Company Let (Formula presented.) be a vector space and (Formula presented.) denote the semigroup (under the composition of maps) of all linear transformations from (Formula presented.) into itself. For a fixed subspace (Formula presented.) of (Formula presented.), let (Formula presented.) be the subsemigroup of (Formula presented.) consisting of all linear transformations on (Formula presented.) which fix all elements in (Formula presented.). In this paper, we describe Green’s relations, regularity and ideals of (Formula presented.); and characterize when (Formula presented.) is factorizable, unit-regular and directly finite, from which the results on (Formula presented.) can be recaptured easily when taking (Formula presented.) as a zero subspace of (Formula presented.). |
format |
Journal |
author |
Yanisa Chaiya Chollawat Pookpienlert Jintana Sanwong |
author_facet |
Yanisa Chaiya Chollawat Pookpienlert Jintana Sanwong |
author_sort |
Yanisa Chaiya |
title |
Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions |
title_short |
Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions |
title_full |
Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions |
title_fullStr |
Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions |
title_full_unstemmed |
Semigroups of linear transformations with fixed subspaces: Green’s relations, ideals and finiteness conditions |
title_sort |
semigroups of linear transformations with fixed subspaces: green’s relations, ideals and finiteness conditions |
publishDate |
2018 |
url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85047971291&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58801 |
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1681425133319749632 |