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Division by Zero in Common Meadows

  • Jan A. Bergstra
  • Alban Ponse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8950)

Abstract

Common meadows are fields expanded with a total multiplicative inverse function. Division by zero produces an additional value denoted with “\({\textup{\textbf{a}}}\)” that propagates through all operations of the meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero that admit a certain cancellation law.

Keywords

Meadow common meadow division by zero additional value abstract datatype 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jan A. Bergstra
    • 1
  • Alban Ponse
    • 1
  1. 1.Section Theory of Computer Science, Informatics Institute, Faculty of ScienceUniversity of AmsterdamThe Netherlands

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