An Objective Representation of the Gaussian Integers
Rings and Algebras
2007-05-23 v2 Commutative Algebra
Category Theory
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.
Cite
@article{arxiv.math/0211454,
title = {An Objective Representation of the Gaussian Integers},
author = {Marcelo Fiore and Tom Leinster},
journal= {arXiv preprint arXiv:math/0211454},
year = {2007}
}
Comments
8 pages. Version 2: application to programming added; journal version