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An Objective Representation of the Gaussian Integers

Marcelo Fiore·Tom Leinster
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Abstract

A rig is a riNg without Negatives. We analyse the free rig on a generator x subject to the equivalence x = 1 + x + x^2, showing that in it the non-constant polynomials form a ring. This ring can be identified with the Gaussian integers, which thus acquire objective meaning.

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Marcelo Fiore, Tom Leinster. 2004-05-13. An Objective Representation of the Gaussian Integers. https://arxiv.org/abs/math/0211454

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