25 citations · 637 across the 113 of their papers we have counts for
12 papers · 1 filter
Universality of Univariate Mixed Fractions in Divisive Meadows
Jan A. Bergstra, Inge Bethke, Dimitri Hendriks
Univariate fractions can be transformed to mixed fractions in the equational theory of meadows of characteristic zero.
Transformation of fractions into simple fractions in divisive meadows
J. A. Bergstra, C. A. Middelburg
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 imposin…
A negative result on algebraic specifications of the meadow of rational numbers
Jan A. Bergstra, Inge Bethke
- the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0…
Fracpairs and fractions over a reduced commutative ring
Jan A. Bergstra, Alban Ponse
In the well-known construction of the field of fractions of an integral domain, division by zero is excluded. We introduce "fracpairs" as pairs subject to laws consistent with the…
Division by zero in non-involutive meadows
J. A. Bergstra, C. A. Middelburg
Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operatio…
Division by zero in common meadows
Jan A. Bergstra, Alban Ponse
Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with "a" that propagates through all operations of the meado…