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On the endomorphism semigroup of an ordered set

1995
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Glasgow Mathematical Journal
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have obtained a remarkable classification of those ordered sets P for which the monoid End P of endomorphisms (i.e. isotone maps) is regular, in the sense that for every / e End P there exists g e End P such that fgf = f. They show that the class of such ordered sets consists precisely of (a) all antichains; (b) all quasi-complete chains; (c) all complete bipartite ordered sets (i.e. given non-zero cardinals a, /3 an ordered set K a p of height 1 having a minimal elements and /3 maximal

doi:10.1017/s0017089500031074
fatcat:ccywiq7mwvaitkvj4urs53kwo4