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- Title
Cancellation Meadows: A Generic Basis Theorem and Some Applications†.
- Authors
Bergstra, Jan A.; Bethke, Inge; Ponse, Alban
- Abstract
Let ℚ0 denote the rational numbers expanded to a ‘meadow’, that is, after taking its zero-totalized form (0−1=0) as the preferred interpretation. In this paper, we consider ‘cancellation meadows’, i.e. meadows without proper zero divisors, such as ℚ0 and prove a generic completeness result. We apply this result to cancellation meadows expanded with differentiation operators, the sign function, and with floor, ceiling and a signed variant of the square root, respectively. We give an equational axiomatization of these operators and thus obtain a finite basis for various expanded cancellation meadows.
- Subjects
VON Neumann regular rings; RATIONAL numbers; SQUARE root; MATHEMATICAL proofs; OPERATOR theory; MATHEMATICAL analysis
- Publication
Computer Journal, 2013, Vol 56, Issue 1, p3
- ISSN
0010-4620
- Publication type
Article
- DOI
10.1093/comjnl/bxs028