2013/06/12 by Vítor H. Fernandes, Fernandes, Vítor H., Preeyanuch Honyam +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #20M10 #20M20 #Advanced Algebra and Logic #Chemical Synthesis and Analysis #FOS: Mathematics #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1306.2774
openalex publication_date 2013/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a finite or infinite chain and let O(X) be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of O(X) and Green's relations on O(X). In fact, more generally, if Y is a nonempty subset of X and O(X,Y) the subsemigroup of O(X) of all elements with range contained in Y, we characterize the largest regular subsemigroup of O(X,Y) and Green's relations on O(X,Y). Moreover, for finite chains, we determine when two semigroups of the type O(X,Y) are isomorphic and calculate their ranks.