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arXiv:0909.2088math.RA

Arithmetical meadows

J. A. Bergstra, C. A. Middelburg

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Abstract

An inversive meadow is a commutative ring with identity equipped with a multiplicative inverse operation made total by choosing 0 as its value at 0. Previously, inversive meadows were shortly called meadows. A divisive meadow is an inversive meadows with the multiplicative inverse operation replaced by a division operation. In the spirit of Peacock's arithmetical algebra, we introduce variants of inversive and divisive meadows without an additive identity element and an additive inverse operation. We give equational axiomatizations of several classes of such variants of inversive and divisive meadows as well as of several instances of them.

arXiv comments
14 pages; sections 4 and 5 permuted
Journal reference
DOI
Subjects
math.RARings and Algebras cs.LOLogic in Computer Science

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  1. Why don't we define “imaginary” numbers for every “impossibility”? (2012) 1 comment

    • Mathematics is a vast subject and I can’t keep track of all developments. In 2010 there was a paper on meadows. I’ve never heard the term before. In that paper it is written: As usual in field theory, the convention to consider p / q as an abbreviation for p · q−1 was used in…

      syzarianView on HNParent context

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