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Isomorphism theorems for octonion planes over local rings


Author: Robert Bix
Journal: Trans. Amer. Math. Soc. 266 (1981), 423-439
MSC: Primary 51A10; Secondary 17C40, 17C50
DOI: https://doi.org/10.1090/S0002-9947-1981-0617543-0
MathSciNet review: 617543
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Abstract: It is proved that there is a collineation between two octonion planes over local rings if and only if the underlying octonion algebras are isomorphic as rings. It is shown that every isomorphism between the little or middle projective groups of two octonion planes over local rings is induced by conjugation with a collineation or a correlation of the planes when the local rings contain $ \frac{1} {2}$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0617543-0
Keywords: Octonion plane, exceptional Jordan algebra
Article copyright: © Copyright 1981 American Mathematical Society

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