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TitleF −semigroups
Author(s)Giraldes, E.
Smith, M. Paula Marques
Mitsch, H.
Natural partial order
Issue date2007
PublisherNational Academy of Sciences of Ukraine
JournalAlgebra and Discrete Mathematics
Citation"Algebra and Discrete Mathematics". 3 (2007) 67-85.
Abstract(s)A semigroup S is called F−semigroup if there exists a group congruence ρ on S such that every ρ −class contains a greatest element with respect to the natural partial order ≤ of S . This generalizes the concept of F−inverse semigroups introduced by V. Wagner in 1961 and investigated by McFadden and O’Caroll in 1971. Five different characterisations of general F−semigroups S are given: by means of residuals, by special principal anticones, by properties of the set of idempotents, by the maximal elements in (S, ≤) and finally, an axiomatic one using an additional unary operation. Also, F−semigroups in special classes are considered; in particular, inflations of semigroups and strong semi- lattices of monoids are studied.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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