Bulg. J. Phys. vol.36 no.s1 (2009), pp. 19-26

Maximal Idempotent Generated Subsemigroups of Ideals of the Semigroup o fAll Isotone Transformations

K. Todorov, J. Koppitz, I. Dimitrova
Faculty of Mathematics and Natural Science, South-West University "Neofit Rilski" Blagoevgrad, 2700, Bulgaria
Abstract. Let Xn = {1,2,...,n} be a finite set, ordered in the usual way. The isotone transformation semigroup On is the set of all order-preserving transformations on Xn, excluding the identity mapping. In this paper we determine the maximal idempotent generated subsemigroups of the ideals of O4. For each proper ideal of On (n ≥3), we characterize two types of maximal idempotent generated subsemigroups.

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