Some Connections Between the Arithmetic and the Geometry of Lipschitz Integers
Abstract
Abstract: Some relationships between the arithmetic and the geometry of Lipschitz and Hurwitz integers are presented. In particular, it is shown that the (ternary) vector product of a Lipschitz integer α with two other Lipschitz integers, both orthogonal to α , is a left and also a right multiple of α , and that the vector product of two left multiples of α with any other Lipschitz integer is still a left multiple of α . We also provide new arithmetical proofs for some old results of Gordon Pall, and raise a geometric problem on the location of some integral quaternions that is related to the factorization of some integers.
Fields of Study & Subjects
Advanced Optimization Algorithms Research
Mathematical and Theoretical Analysis
Polynomial and algebraic computation
Publication details
- Journal / source
- Mathematical Proceedings of the Royal Irish Academy
- Volume
- 126A
- Issue
- 1
- Pages
- 1–14
- Publication date
- 1 January 2026
- Language
- EN