A semigroup $S$ is called a generalized $F$ -semigroup if there exists a group congruence on $S$ such that the identity class contains a greatest element with respect to the natural partial order $\leq_{S}$ of $S$ . Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup $(S, \cdot, \leq_{S})$ are determined. It is shown that a semigroup $S$ is a generalized $F$ -semigroup if and only if $S$ contains an anticone, which is a principal order ideal of $(S, \leq_{S})$ . Also a characterization by means of the structure...

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Decomposition of a semiring into division semirings

Perfect elements in Dubreil-Jacotin regular semigroups.

Embedding finite semigroups in finite semibands of minimal depth.

Generalized F -semigroups

Generalized $F$ -semigroups