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  TITLE:    <em>The Max-Sum Algebra of the Natural Numbers has no Finite
  Equational Basis</em> <p>

  SPEAKER:  Anna Ingólfsdóttir, BRICS, Aalborg University
<p>

  DATE: Friday, 9 April 1999<p>

  PLACE and TIME: Room E3-209 at 14:00. <p>

  ABSTRACT:  <p>

  In this talk, I shall show that the collection of identities which
   hold in the
  algebra <b>N</b> of the natural numbers with constant zero, and
  binary operations of sum and maximum is not finitely based.
  Moreover, I shall argue that, for every <em>n</em>, the equations in at most
  <em>n</em> variables that hold in that algebra do not form an equational
  basis.  As a stepping stone in the proof of these results, several
  results of independent interest will be presented. In particular,
  explicit descriptions of the free algebras in the variety generated
  by <b>N</b> are offered.  Such descriptions are based upon a
  geometric characterization of the equations that hold in <b>N</b>. <p>

This talk is based upon joint work with Luca Aceto (BRICS, Aalborg)
and Zoltan Esik (University of Szeged).