25 citations · 637 across the 113 of their papers we have counts for
Showing 2014 · math.RAShow all
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math.RA2014★ 25 cited
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…
math.RA2014★ 9 cited
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…
math.RA2014★ 2 cited
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…