Fracpairs and fractions over a reduced commutative ring
The original motivation of this paper comes from the datatypes in computer science, but we face a nice small work in algebra and logic. Fraction fields over domains are defined so that the denominator is not allowed to be zero. In the present generalization of the field of fractions, the ring is only supposed to be commutative and not to contain nilpotent elements and the denominator equal zero is permited. So, one can compute with fractions (fracpairs) over \(\mathbb Z _6\) and \(\frac{1}{0}\) so as \(\frac{2}{0}\) are legal elements of the resulting meadow. The structures studied are kept equational, and most of the discussion focusses on term rewriting.
scientific article; zbMATH DE number 6595325