Abstract
A semigroup S is called F-monoid if S has an identity and if there exists a group congruence ρ on S such that each ρ-class of S contains a greatest element with respect to the natural partial order of S (see Mitsch, 1986). Generalizing results given in Giraldes et al. (2004) and specializing some of Giraldes et al. (Submitted) five characterizations of such monoids S are provided. Three unary operations “*”, “○”, and “ − ” on S defined by means of the greatest elements in the different ρ-classes of S are studied. Using their properties a charaterization of F-monoids S by their regular part S° = {a°|a ∈ S} and the associates of elements in S° is given. Under the hypothesis that S * = {a *|a ∈ S} is a subsemigroup it is shown that S is regular, whence of a known structure (see Giraldes et al., 2004).
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