Axioms for function semigroups with agreement quasi-order
Stokes, T.E. (2011). Axioms for function semigroups with agreement quasi-order. Algebra Universalis, 66(1-2), 85-98.
Permanent Research Commons link: http://hdl.handle.net/10289/5859
The agreement quasi-order on pairs of (partial) transformations on a set X is defined as follows: (f, g) ≼ (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 ∩-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.