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dc.contributor.authorStokes, Tim E.en_NZ
dc.date.accessioned2018-06-12T03:13:02Z
dc.date.available2018en_NZ
dc.date.available2018-06-12T03:13:02Z
dc.date.issued2018en_NZ
dc.identifier.citationStokes, T. E. (2018). Generalised domain and E-inverse semigroups. Semigroup Forum, Online First. https://doi.org/10.1007/s00233-018-9917-6en
dc.identifier.issn0037-1912en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/11889
dc.description.abstractA generalised D-semigroup is here defined to be a left E-semiabundant semigroup S in which the \overline{\mathcal R}_E-class of every x\in S contains a unique element D(x) of E, made into a unary semigroup. Two-sided versions are defined in the obvious way in terms of \overline{\mathcal R}_E and \overline{\mathcal L}_E. The resulting class of unary (bi-unary) semigroups is shown to be a finitely based variety, properly containing the variety of D-semigroups (defined in an order-theoretic way in Communications in Algebra, 3979–4007, 2014). Important subclasses associated with the regularity and abundance properties are considered. The full transformation semigroup T_X can be made into a generalised D-semigroup in many natural ways, and an embedding theorem is given. A generalisation of inverse semigroups in which inverses are defined relative to a set of idempotents arises as a special case, and a finite equational axiomatisation of the resulting unary semigroups is given.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherSpringeren_NZ
dc.rights© 2018 Springer US. This is the author's accepted version. The final publication is available at Springer via dx.doi.org/10.1007/s00233-018-9917-6.
dc.subjectmathematicsen_NZ
dc.subjectE-semiabundant semigroupen_NZ
dc.subjectD-semigroupen_NZ
dc.subjectregular semigroupen_NZ
dc.subjectE-semiabundant semigroup
dc.subjectD-semigroup
dc.subjectregular semigroup
dc.titleGeneralised domain and E-inverse semigroupsen_NZ
dc.typeJournal Article
dc.identifier.doi10.1007/s00233-018-9917-6en_NZ
dc.relation.isPartOfSemigroup Forumen_NZ
pubs.elements-id217429
pubs.publication-statusPublished onlineen_NZ
pubs.volumeOnline Firsten_NZ
dc.identifier.eissn1432-2137en_NZ


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