Left and Right Regular Elements of Some Subsemigroups of the Linear Transformations Semigroups with Invariant Subspace

Authors

  • Nares Sawatraksa Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University
  • Piyaporn Tantong Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan, Thailand

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5623

Keywords:

left regular, right regular, linear transformation, invariant subspace

Abstract

In this paper, we investigate the left regularity, right regularity, and complete regularity of elements in subsemigroups of the semigroups of linear transformations with invariant subspaces. We provide necessary and sufficient conditions for these subsemigroups to be left regular, right regular, and completely regular. Specifically, we examine semigroups of linear transformations with restricted range, invariant subspaces, and fixed subspaces. The results offer a comprehensive characterization of regular elements within these algebraic structures and extend existing work in this field. Our findings have potential applications in algebraic theory, particularly in the study of transformation semigroups and their subsemigroups.

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Published

2025-01-31

Issue

Vol. 18 No. 1: (January 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Nares Sawatraksa, Piyaporn Tantong

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How to Cite

Left and Right Regular Elements of Some Subsemigroups of the Linear Transformations Semigroups with Invariant Subspace. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5623. https://doi.org/10.29020/nybg.ejpam.v18i1.5623