Some Arithmetical Semigroups

  • A. S. Fraenkel
  • H. Porta
  • K. B. Stolarsky
Chapter
Part of the Progress in Mathematics book series (PM, volume 85)

Abstract

The peculiar multiplication rule is asssociative but does not always produce an integer for integers
$$ n\,x\,m\, = \,\left\lfloor {\left( {\frac{3}{2}} \right)\,nm} \right\rfloor $$
n and m. If we try to force the result to be an integer by truncation, i. e., by
$$ n\,x\,m\, = \,\left\lfloor {\left( {\frac{3}{2}} \right)\,nm} \right\rfloor $$
we no longer have an associative multiplication. For example (3 x (5 x 7)) = 234. It would seem exceptional to find associativity in operations whose definition involves truncation. Our object is to study several such exceptional operations.

Keywords

Argentina 

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Copyright information

© Bikhäuser Boston 1990

Authors and Affiliations

  • A. S. Fraenkel
    • 1
  • H. Porta
    • 2
  • K. B. Stolarsky
    • 1
  1. 1.Dept. of Applied MathematicsThe Weizman Institute of ScienceRehovotIsreal
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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