@article{Sangkhanan2025, 
author = {Kritsada Sangkhanan},
title = {Semigroups of partial linear transformations whose restrictions belong to an injective partial linear transformation semigroup},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29470-29487},
keywords = {partial linear transformation semigroup, injective partial linear transformation semigroup, Green's relations, regularity, ideals},
url = {https://www.sciopen.com/article/10.3934/math.20251294},
doi = {10.3934/math.20251294},
abstract = {Let    V be a vector space over a field        F   and let    W be a subspace of    V. The semigroup of partial linear transformations on    V whose restriction to    W belongs to an injective partial linear transformation semigroup        I    (  W  ) is denoted by        P                  I            (      W      )        (  V  ). In this paper, we describe Green's relations for        P                  I            (      W      )        (  V  ), characterize its regular elements, and give necessary and sufficient conditions for        P                  I            (      W      )        (  V  ) to be regular, inverse, or completely regular. We also analyze the ideal structure of        P                  I            (      W      )        (  V  ), identifying its maximal and minimal ideals.}
}