Cancellation Meadows: a Generic Basis Theorem and Some Applications
Abstract
Let Q_0 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 $Q_0$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2008
- DOI:
- 10.48550/arXiv.0803.3969
- arXiv:
- arXiv:0803.3969
- Bibcode:
- 2008arXiv0803.3969B
- Keywords:
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- Mathematics - Rings and Algebras;
- Computer Science - Logic in Computer Science;
- AC;
- RA
- E-Print:
- 24 pages, 6 tables