Quadratic Jordan algebras whose elements are all invertible or nilpotent
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- by Kevin McCrimmon
- Proc. Amer. Math. Soc. 35 (1972), 309-316
- DOI: https://doi.org/10.1090/S0002-9939-1972-0308217-4
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Abstract:
We prove that if $\mathfrak {J}$ is a unital quadratic Jordan algebra whose elements are all either invertible or nilpotent, then modulo the nil radical $\mathfrak {N}$ the algebra $\mathfrak {J}/\mathfrak {N}$ is either a division algebra or the Jordan algebra determined by a traceless quadratic form in characteristic 2. We also show that if $\mathfrak {U}$ is an associative algebra with involution whose symmetric elements are either invertible or nilpotent, then modulo its radical $\mathfrak {U}/\Re$ is a division algebra, a direct sum of anti-isomorphic division algebras, or a split quaternion algebra.References
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Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 309-316
- MSC: Primary 17A15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0308217-4
- MathSciNet review: 0308217