On semigroups of endomorphisms of a chain with restricted range

• Main Authors: Fernandes V.H., Honyam P., Quinteiro T.M., Singha B.
• Format: Article
• Language: English
• Published: 2014
• Online Access: http://www.scopus.com/inward/record.url?eid=2-s2.0-84887266823&partnerID=40&md5=b976cf83af907df491d5a861d23d66f8; http://cmuir.cmu.ac.th/handle/6653943832/7240
• Institution: Chiang Mai University

Let X be a finite or infinite chain and let {Mathematical expression} be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of {Mathematical expression} and Green's relations on {Mathematical expression}. In fact, more generally, if Y is a nonempty subset of X and {Mathematical expression} is the subsemigroup of {Mathematical expression} of all elements with range contained in Y, we characterize the largest regular subsemigroup of {Mathematical expression} and Green's relations on {Mathematical expression}. Moreover, for finite chains, we determine when two semigroups of the type {Mathematical expression} are isomorphic and calculate their ranks. © 2013 Springer Science+Business Media New York.