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Natural partial order and finiteness conditions on semigroups of linear transformations with invariant subspaces

  • Yanisa ChaiyaEmail author
Research Article
  • 16 Downloads

Abstract

Given a vector space V and a subspace W of V, we consider the semigroup (under composition) S(VW), consisting of all linear transformations on V which leave the subspace W invariant. In this paper, we characterize the natural partial order on S(VW). In the partially ordered set, we determine the compatibility of their elements, and find all maximal and minimal elements. Also, we give necessary and sufficient conditions for S(VW) to be factorizable, unit-regular and directly finite.

Keywords

Linear transformation semigroup Invariant subspace Natural partial order Finiteness condition 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Faculty of Science and TechnologyThammasat University (Rangsit Campus)Pathum ThaniThailand

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