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      Axioms for function semigroups with agreement quasi-order

      Stokes, Tim E.
      DOI
       10.1007/s00012-011-0152-1
      Link
       www.springerlink.com
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      Citation
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      Stokes, T.E. (2011). Axioms for function semigroups with agreement quasi-order. Algebra Universalis, 66(1-2), 85-98.
      Permanent Research Commons link: https://hdl.handle.net/10289/5859
      Abstract
      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.
      Date
      2011
      Type
      Journal Article
      Publisher
      Springer
      Collections
      • Computing and Mathematical Sciences Papers [1454]
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