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- W2247158867 abstract "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 $le _{S}$ of $S$. Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup $(S,cdot ,le _{S})$ 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 $(S,le _{S})$. Also a characterization by means of the structure of the set of idempotents or by the existence of a particular element in $S$ is given. The generalized $F$-semigroups in the following classes are described: monoids, semigroups with zero, trivially ordered semigroups, regular semigroups, bands, inverse semigroups, Clifford semigroups, inflations of semigroups, and strong semilattices of monoids." @default.
- W2247158867 created "2016-06-24" @default.
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- W2247158867 date "2005-01-01" @default.
- W2247158867 modified "2023-09-26" @default.
- W2247158867 title "Generalized $F$-semigroups" @default.
- W2247158867 doi "https://doi.org/10.21136/mb.2005.134136" @default.
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