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A Note on Complex Algebras of Semigroups

  • Peter Jipsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)

Abstract

The main result is that the variety generated by complex algebras of (commutative) semigroups is not finitely based. It is shown that this variety coincides with the variety generated by complex algebras of partial (commutative) semigroups. An example is given of an 8-element commutative Boolean semigroup that is not in this variety, and an analysis of all smaller Boolean semigroups shows that there is no smaller example. However, without associativity the situation is quite different: the variety generated by complex algebras of (commutative) binars is finitely based and is equal to the variety of all Boolean algebras with a (commutative) binary operator.

Keywords

Boolean Algebra Binary Operator Equational Theory Relation Algebra Algebraic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Peter Jipsen
    • 1
  1. 1.Chapman UniversityOrangeUSA

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