Please use this identifier to cite or link to this item: http://cmuir.cmu.ac.th/jspui/handle/6653943832/53664
Title: On semigroups of endomorphisms of a chain with restricted range
Authors: Vítor H. Fernandes
Preeyanuch Honyam
Teresa M. Quinteiro
Boorapa Singha
Keywords: Mathematics
Issue Date: 1-Aug-2014
Abstract: © 2013, Springer Science+Business Media New York. Let X be a finite or infinite chain and let ${\mathcal{O}}(X)$ be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of ${\mathcal{O}}(X)$ and Green’s relations on ${\mathcal{O}}(X)$. In fact, more generally, if Y is a nonempty subset of X and ${\mathcal{O}}(X,Y)$ is the subsemigroup of ${\mathcal{O}}(X)$ of all elements with range contained in Y, we characterize the largest regular subsemigroup of ${\mathcal{O}}(X,Y)$ and Green’s relations on ${\mathcal{O}}(X,Y)$. Moreover, for finite chains, we determine when two semigroups of the type ${\mathcal {O}}(X,Y)$ are isomorphic and calculate their ranks.
URI: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942193328&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/53664
ISSN: 00371912
Appears in Collections:CMUL: Journal Articles

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