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dc.contributor.authorJackson, Marcel
dc.contributor.authorStokes, Tim E.
dc.identifier.citationJackson, M., & Stokes, T. (2013). On representing semigroups with subsemilattices. Journal of Algebra, 376, 228-260.en_NZ
dc.description.abstractWe examine the problem of representing semigroups as binary relations, partial maps and injective functions, with the constraint that certain pre-designated idempotent elements must be represented as restrictions of the identity function. Appropriately formulated, the corresponding classes of representable structures is a quasivariety, but we show that they cannot be finitely axiomatised in first order logic. Quite a few algebraic structures have both a semigroup reduct and the ability to distinguish certain idempotent elements, and we use our construction to show that representability for these is also not finitely axiomatisable. Amongst the classes covered are subsemigroups of weakly left ample semigroups, various classes of ordered semigroups, semigroups of various kinds of binary relation with fixset operation. We also give new proofs of the nonfinite axiomatisability of the class of semigroups of binary relations endowed with domain and/or range operations, and of subsemigroups of inverse semigroups.en_NZ
dc.relation.ispartofJournal of Algebra
dc.subjectpartial mapsen_NZ
dc.subjectrelation algebrasen_NZ
dc.subjectsemigroups of functionsen_NZ
dc.titleOn representing semigroups with subsemilatticesen_NZ
dc.typeJournal Articleen_NZ
dc.relation.isPartOfJournal of Algebraen_NZ

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