Axioms for function semigroups with agreement quasi-order.
The agreement quasi-order \(\preccurlyeq\) on pairs of partial transformations on a set \(X\) is defined by \((f,g)\preccurlyeq(h,k)\) if whenever \(f\) and \(g\) are defined and agree, so do \(h\) and \(k\). The paper axiomatizes function semigroups (and monoids) \(S\) with this quasi-order through a list of six axioms on the order ideals generated by pairs \((s,t)\) in \(S\times S\) under this quasi-order. Finite axiomizations are obtained for groups and for inverse semigroups of injective functions equipped with the quasi order of fixed set inclusion.
scientific article; zbMATH DE number 5977544
scientific article