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dc.contributor.authorStokes, Tim E.en_NZ
dc.date.accessioned2022-06-12T23:36:17Z
dc.date.available2022-06-12T23:36:17Z
dc.date.issued2022en_NZ
dc.identifier.issn0037-1912en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/14914
dc.description.abstractOn a semigroup S, define the equivalence relation F={(a,b)∈S×S∣∀x∈S:xa=x⇔xb=x}, and define G dually. We say S is F-abundant if there is an idempotent in every F-class, and similarly for G-abundance, and we say S is (F,G)-abundant if it is both F-abundant and G-abundant. These concepts are analogous to the notions of regularity and one- and two-sided abundance, defined in terms of Green’s relations L and R, and their generalisations L∗ and R∗, respectively. We relate this new form of abundance to the earlier ones, considering in particular the analogs of superabundance and amiability.
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherSpringeren_NZ
dc.rights© 2022 Springer Nature Switzerland AG.This is the author's accepted version. The final publication is available at Springer via dx.doi.org/10.1007/s00233-021-10246-2
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematicsen_NZ
dc.subjectRegularen_NZ
dc.subjectAbundanten_NZ
dc.subjectSuperabundanten_NZ
dc.subjectAmiableen_NZ
dc.title(F,G)-abundant semigroupsen_NZ
dc.typeJournal Article
dc.identifier.doi10.1007/s00233-021-10246-2en_NZ
dc.relation.isPartOfSemigroup Forumen_NZ
pubs.begin-page180
pubs.elements-id267460
pubs.end-page194
pubs.issue1en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume104en_NZ
dc.identifier.eissn1432-2137en_NZ


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