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Software, Services, and Systems pp 46–61Cite as

Division by Zero in Common Meadows

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Part of the Lecture Notes in Computer Science book series (LNPSE,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

This paper is dedicated to Martin Wirsing on the occasion of his emeritation; an earlier version appeared as report arXiv:1406.6878v1 [math.RA], 26 June 2014.

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Authors and Affiliations

  1. Section Theory of Computer Science, Informatics Institute, Faculty of Science, University of Amsterdam, The Netherlands

    Jan A. Bergstra & Alban Ponse

Authors
  1. Jan A. Bergstra
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  2. Alban Ponse
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Editor information

Editors and Affiliations

  1. IMT Institute for Advanced Studies Lucca, Piazza S. Francesco, 19, 55100, Lucca, Italy

    Rocco De Nicola

  2. Ludwig-Maximilians-Universität München, Germany

    Rolf Hennicker

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Bergstra, J.A., Ponse, A. (2015). Division by Zero in Common Meadows. In: De Nicola, R., Hennicker, R. (eds) Software, Services, and Systems. Lecture Notes in Computer Science, vol 8950. Springer, Cham. https://doi.org/10.1007/978-3-319-15545-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-15545-6_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15544-9

  • Online ISBN: 978-3-319-15545-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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