On semigroups of endomorphisms of a chain with restricted range - Fernandes V.H. (2014)
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.