Naturally ordered transformation semigroups preserving an equivalence relation on an invariant set
Year: 2025
Type: article
Abstract: For a nonempty set X, let T(X) represent the full transformation semigroup on X. Given a nonempty subset Y of X and an equivalence relation E defined on X, we consider the set S_E(X,Y) = {α ∈T(X) : ∀x,y ∈ Y,(x,y) ∈ E ⇒ (xα,yα) ∈ E,xα,yα ∈ Y}. Then S_E(X,Y) is a subsemigroup of T(X). In this paper, we provide a characterization of the natural partial order on S_E(X,Y). Moreover, we investigate the elements within S_E(X,Y ) which are minimal, maximal right-compatible, and left-compatible with respect to such order.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4415436620