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      Identities in the Algebra of Partial Maps

      Jackson, Marcel; Stokes, Tim E.
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      AlgebraPartialEqTheoryFinal.pdf
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      DOI
       10.1142/S0218196706003426
      Link
       www.worldscinet.com
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      Citation
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      Jackson, M. & Stokes, T. E.(2006) Identities in the algebra of partial maps. International Journal of Algebra and Computation, 16(6), 1131-1159.
      Permanent Research Commons link: https://hdl.handle.net/10289/2007
      Abstract
      We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.
      Date
      2006
      Type
      Journal Article
      Publisher
      World Scientific Publishing
      Rights
      This is an author’s version of an article published in the journal: International Journal of Algebra and Computation. ©2006 World Scientific Publishing Company, http://www.worldscinet.com/ijac/ijac.shtml
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      • Computing and Mathematical Sciences Papers [1454]
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