An Objective Representation of the Gaussian Integers
Marcelo Fiore, Tom Leinster
Abstract
A rig is a riNg without Negatives. We analyse the free rig on a generator x subject to the equivalence x = 1 + x + x2, 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.
Create a lesson
Related papers
On Jordan nilpotency of index n in group rings
Osnel B. Cristo, Mariana G. Cornelissen, Rodrigo L. Rodrigues
High-Degree Restricted Cohomology for K(3;1)(1) in Characteristics Five and Seven
Chao Ma
Identities of Representation of Lie subalgebras of the first Weyl algebra
Vyacheslav Futorny, Plamen Koshlukov, João Fernando Schwarz
Homology and Topology of Partially Ordered Fields
Hanzhen Bao
Hopf algebra polynomial identities in the Sweedler algebra
Alexey Gordienko, Maria Morozova
Resolvent comparison for Hermitian block matrices and Kelmans transformations
Xianhao Meng, Zhijun Xu, Zhiyuan Zhang