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arXiv:1406.6878math.RA

Division by zero in common meadows

Jan A. Bergstra, Alban Ponse

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Abstract

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 meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero that admit a certain cancellation law.

arXiv comments
17 pages, 4 tables; differences with v3: axiom (14) of Mda (Table 2) has been replaced by the stronger axiom (12), this appears to be necessary for the proof of Theorem 3.2.1
Journal reference
DOI
Subjects
math.RARings and Algebras

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