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Communications in Algebra Volume 28, 2000 - Issue 7

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Original Articles

Alternative rings of small order

Edgar G. Goodaire Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, A1C 5S7, CanadaCorrespondence[email protected]

Yongxin Zhou Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, A1C 5S7, CanadaCorrespondence[email protected]

Pages 3335-3349 | Received 01 Mar 1999, Published online: 27 Jun 2007

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https://doi.org/10.1080/00927870008827029

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Abstract

We construct all the alternative (but not associative) algebras of dimension at most 5 over a perfect field. For any prime p, we show that there are fifteen alternative rings of prime power order pⁿ ,n≤5, which are not associative. None of these rings is nil. Just one has a unity.

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