Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/11143

TitleF −semigroups
Author(s)Giraldes, E.
Smith, M. Paula Marques
Mitsch, H.
KeywordsSemigroup
Congruence
Natural partial order
Anticones
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.
TypeArticle
URIhttp://hdl.handle.net/1822/11143
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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