Fracpairs and fractions over a reduced commutative ring

DOI10.1016/J.INDAG.2016.01.007zbMath1348.13012arXiv1411.4410OpenAlexW2269907218MaRDI QIDQ297980

Alban Ponse, Jan A. Bergstra

Publication date: 20 June 2016

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.4410

zbMATH Keywords

term rewritingabstract datatypecommon meadowdivision by zerofraction as a pairrational numbers

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Grammars and rewriting systems (68Q42) Structure, classification theorems for modules and ideals in commutative rings (13C05)

Related Items (6)

Partial arithmetical data types of rational numbers and their equational specification ⋮ Unnamed Item ⋮ Arithmetical datatypes with true fractions ⋮ Eager Equality for Rational Number Arithmetic ⋮ Symmetric transrationals: the data type and the algorithmic degree of its equational theory ⋮ The wheel of rational numbers as an abstract data type

Cites Work

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• Inversive meadows and divisive meadows
• Termination orderings for associative-commutative rewriting systems
• The rational numbers as an abstract data type
• Equational specifications, complete term rewriting systems, and computable and semicomputable algebras
• Rewrite systems for natural, integral, and rational arithmetic
• The initial meadows
• Division by Zero in Common Meadows

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