English

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

R2 v1 2026-07-22T16:49:51.582Z