Abstract
The agreement quasi-order on pairs of (partial) transformations on a set X is defined as follows: \({(f, g) \preceq (h, k)}\) if whenever f, g are defined and agree, so do h, k. We axiomatize function semigroups and monoids equipped with this quasi-order, thereby providing a generalisation of first projection quasi-ordered \({\cap}\) -semigroups of functions. As an application, axiomatizations are obtained for groups and inverse semigroups of injective functions equipped with the quasi-order of fix-set inclusion. All axiomatizations are finite.
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Presented by M. G. Jackson.
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Stokes, T. Axioms for function semigroups with agreement quasi-order. Algebra Univers. 66, 85 (2011). https://doi.org/10.1007/s00012-011-0152-1
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DOI: https://doi.org/10.1007/s00012-011-0152-1