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Advisor(s)
Abstract(s)
Let X be a finite or infinite chain and let be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of and Green's relations on. In fact, more generally, if Y is a nonempty subset of X and is the subsemigroup of of all elements with range contained in Y, we characterize the largest regular subsemigroup of and Green's relations on. Moreover for finite chains, we determine when two semigroups of the type are isomorphic and calculate their ranks.
Description
Keywords
Transformations Order-Preserving Restricted Range Rank
Citation
FERNANDES, Vítor H.; [et al] – On semigroups of endomorphisms of a chain with restricted range. Semigroup Forum. ISSN: 0037-1912. Vol. 89, nr. 1 (2014), pp. 77-104
Publisher
Springer