Fracpairs and fractions over a reduced commutative ring
type: Item
instance of: scholarly article
title: Fracpairs and fractions over a reduced commutative ring
zbMATH Open document ID: 1348.13012
author: J. A. Bergstra
author: Alban Ponse
published in: Indagationes Mathematicae. New Series
publication date: 2016-06-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1411.4410
review text: 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.
reviewed by: Mihai Prunescu
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 68Q42
Mathematics Subject Classification ID: 16S15
zbMATH DE Number: 6595325
zbMATH Keywords: fraction as a pair
zbMATH Keywords: common meadow
zbMATH Keywords: division by zero
zbMATH Keywords: abstract datatype
zbMATH Keywords: rational numbers
zbMATH Keywords: term rewriting
MaRDI profile type: Publication
OpenAlex ID: W2269907218
arXiv ID: 1411.4410
cites work: Termination orderings for associative-commutative rewriting systems
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cites work: Q3992979
DOI: 10.1016/J.INDAG.2016.01.007
description: scientific article; zbMATH DE number 6595325