Endomorphisms of semigroups of monotone transformations
De Biao Li, V\'itor H. Fernandes
TL;DR
This paper characterizes the structure of endomorphisms of semigroups consisting of all monotone transformations, partial transformations, and permutations on finite chains, providing a comprehensive algebraic analysis.
Contribution
It provides a complete description of the endomorphism monoids for various semigroups of monotone transformations on finite chains, a novel algebraic characterization.
Findings
Characterization of endomorphisms of all monotone full transformations
Description of endomorphisms of monotone partial transformations
Analysis of endomorphisms of monotone partial permutations
Abstract
In this paper, we characterize the monoid of endomorphisms of the semigroup of all monotone full transformations of a finite chain, as well as the monoids of endomorphisms of the semigroup of all monotone partial transformations and of the semigroup of all monotone partial permutations of a finite chain.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Fuzzy and Soft Set Theory