اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCancellation Meadows: a Generic Basis Theorem and Some Applications
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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.
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