منابع مشابه
Inversive meadows and divisive meadows
An inversive meadow is a commutative ring with identity and a total multiplicative inverse operation satisfying 0 = 0. Previously, inversive meadows were shortly called meadows. In this paper, we introduce divisive meadows, which are inversive meadows with the multiplicative inverse operation replaced by a division operation. We introduce a translation from the terms over the signature of divis...
متن کاملUniversality of Univariate Mixed Fractions in Divisive Meadows
Univariate fractions can be transformed to mixed fractions in the equational theory of meadows of characteristic zero.
متن کاملTransformation of fractions into simple fractions in divisive meadows
Meadows are alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Divisive meadows are meadows with the multiplicative inverse operation replaced by a division operation. Viewing a fraction as a term over the signature of divisive m...
متن کاملArithmetical meadows
An inversive meadow is a commutative ring with identity equipped with a total multiplicative inverse operation satisfying 0 −1 = 0. Previously, inversive meadows were shortly called meadows. A divisive meadow is an inversive meadows with the multiplicative inverse operation replaced by a division operation. In the spirit of Peacock's arithmetical algebra, we introduce variants of inversive and ...
متن کاملDifferential Meadows
A meadow is a zero totalised field (0 = 0), and a cancellation meadow is a meadow without proper zero divisors. In this paper we consider differential meadows, i.e., meadows equipped with differentiation operators. We give an equational axiomatization of these operators and thus obtain a finite basis for differential cancellation meadows. Using the Zariski topology we prove the existence of a d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Logic
سال: 2011
ISSN: 1570-8683
DOI: 10.1016/j.jal.2011.03.001