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Factorization and congruence in the arithmetics of Cayley's algebra

Published online by Cambridge University Press:  18 May 2009

P. J. C. Lamont
P. J. C. Lamont
Affiliation:
Department of Computer Science, College of Applied Sciences, Western Illinois University, Macomb, Illinois 61455
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This paper treats factorization and congruence in the arithmetics of Cayley's algebra C. Results, proved by Rankin [10], on the number of factorizations of a given element in the nonmaximal arithmetics Ho and Jo are reviewed. Further, new results on congruence are established and are used to find the number of factorizations of a prescribed element in the remaining arithmetics, including the maximal arithmetics Jw When computer factorizing a given element, the congruence results can be used as a heuristic device to prune the search tree.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 2 , May 1991 , pp. 171 - 180
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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