On the Two-Variable Fragment of the Equational Theory of the Max-Sum Algebra of the Natural Numbers

  • Luca Aceto
  • Zoltán Ésik
  • Anna Ingólfsdóttir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1770)


This paper shows that the collection of identities in two variables which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum does not have a finite equational axiomatization. This gives an alternative proof of the nonexistence of a finite basis for N—a result previously obtained by the authors.


Partial Order Equational Theory Axiom System Free Algebra Constant Zero 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Luca Aceto
    • 1
  • Zoltán Ésik
    • 2
  • Anna Ingólfsdóttir
    • 2
  1. 1.BRICS, Department of Computer ScienceAalborg UniversityAalborg ØDenmark
  2. 2.Department of Computer ScienceA. József UniversitySzegedHungary

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