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. FernandesPreeyanuch HonyamTeresa M. QuinteiroBoorapa 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=inwardhttp://cmuir.cmu.ac.th/jspui/handle/6653943832/53664 ISSN: 00371912 Appears in Collections: CMUL: Journal Articles

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