Some Connections Between The Arithmetic and The Geometry of Lipschitz Integers

Details Some Connections Between The Arithmetic and The Geometry of Lipschitz Integers Some Connections Between The Arithmetic and The Geometry of Lipschitz Integers

2012-01-27

arxiv.org/abs/1201.5817v1

Mathematics

Number Theory

Scientific paper

Some relationships between the arithmetic and the geometry of Lipschitz and Hurwitz integers are here presented. In particular, it is shown that the vector product of two left multiples of a Lipschitz integer $\alpha$ with any other Lipschitz integer is still a left multiple of $\alpha$, and that the vector product of a Lipschitz integer $\alpha$ with two other such integers orthogonal to it is both a left and a right multiple of $\alpha$.

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