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Semigroups of partial linear transformations whose restrictions belong to an injective partial linear transformation semigroup
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Journal Article
Semigroups of partial linear transformations whose restrictions belong to an injective partial linear transformation semigroup
2025
Overview
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 PI(W)(V) . In this paper, we describe Green's relations for PI(W)(V) , characterize its regular elements, and give necessary and sufficient conditions for PI(W)(V) to be regular, inverse, or completely regular. We also analyze the ideal structure of PI(W)(V) , identifying its maximal and minimal ideals.
Publisher
American Institute of Mathematical Sciences
Subject
