Arithmetical meadows

Report, Preprint OPEN
Bergstra, J. A.; Middelburg, C. A.;
(2009)
  • Publisher: arXiv.org
  • Subject: Mathematics - Rings and Algebras | 12E12, 12E30, 12L05 | Computer Science - Logic in Computer Science
    arxiv: Computer Science::Logic in Computer Science | Mathematics::Rings and Algebras

An inversive meadow is a commutative ring with identity equipped with a multiplicative inverse operation made total by choosing 0 as its value at 0. Previously, inversive meadows were shortly called meadows. A divisive meadow is an inversive meadows with the multiplicat... View more
  • References (17)
    17 references, page 1 of 2

    1. Bergstra, J.A., Bethke, I.: Square root meadows. arXiv:0901.4664v1 [cs.LO] at http://arxiv.org/ (2009)

    2. Bergstra, J.A., Hirshfeld, Y., Tucker, J.V.: Meadows and the equational specification of division. Theoretical Computer Science 410(12-13), 1261-1271 (2009)

    3. Bergstra, J.A., Middelburg, C.A.: Inversive meadows and divisive meadows. Electronic Report PRG0907, Programming Research Group, University of Amsterdam (2009). Available from http://www.science.uva.nl/research/prog/ publications.html. Also available from http://arxiv.org/: arXiv:0907.0540v2 [math.RA]

    4. Bergstra, J.A., Ponse, A.: Differential meadows. arXiv:0804.3336v1 [math.RA] at http://arxiv.org/ (2008)

    5. Bergstra, J.A., Ponse, A.: A generic basis theorem for cancellation meadows. arXiv:0803.3969v2 [math.RA] at http://arxiv.org/ (2008)

    6. Bergstra, J.A., Tucker, J.V.: Algebraic specifications of computable and semicomputable data types. Theoretical Computer Science 50(2), 137-181 (1987)

    7. Bergstra, J.A., Tucker, J.V.: Equational specifications, complete term rewriting, and computable and semicomputable algebras. Journal of the ACM 42(6), 1194- 1230 (1995)

    8. Bergstra, J.A., Tucker, J.V.: The rational numbers as an abstract data type. Journal of the ACM 54(2), Article 7 (2007)

    9. Goodearl, K.R.: Von Neumann Regular Rings. Pitman, London (1979)

    10. Kleiner, I.: A historically focused course in abstract algebra. Mathematics Magazine 71(2), 105-111 (1998)

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