Stokes, Tim E.2022-06-122022-06-1220220037-1912https://hdl.handle.net/10289/14914On 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.application/pdfen© 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/s00233-021-10246-2Science & TechnologyPhysical SciencesMathematicsRegularAbundantSuperabundantAmiableJournal Article10.1007/s00233-021-10246-21432-2137