A Generic Basis Theorem for Cancellation Meadows

Details A Generic Basis Theorem for Cancellation Meadows A Generic Basis Theorem for Cancellation Meadows

2008-03-27

arxiv.org/abs/0803.3969v2

Mathematics

Rings and Algebras

16 pages, 3 tables

Scientific paper

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 $Q_0$. We prove a representation result and a generic completeness result. We apply these results to cancellation meadows extended with the sign function, and with floor and ceiling, respectively.

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