Axioms for function semigroups with agreement quasi-order
Tóm tắt
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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