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AAA76 - 76th Workshop on General Algebra (76. Arbeitstagung Allgemeine Algebra)
May 22-25, 2008
Department of Algebra, Johannes Kepler University Linz
Linz, Austria

Organizers
Erhard Aichinger, Peter Mayr, Matt Nickodemus, Günter Pilz

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An application of the ring of integer quaternions
by
Emil W. Kiss
Department of Algebra and Number Theory, Eotvos University, Budapest
Coauthors: Lee M. Goswick, Nandor Simanyi (University of Birmingham, Alabama, USA), Gabor Moussong (Department of Geometry, Eotvos University)

We investigate, using irreducible integer quaternions, cubic lattices in the 3-dimensional real euclidean space that are spanned by three pairwise orthogonal vectors of equal length that have integer coordinates. A relationship to Euler's famous numeri idonei is explored. Higher dimensional analogues of our results are stated as open problems.

Date received: May 14, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawc-65.