Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quadratic Jordan algebras whose elements are all invertible or nilpotent


Author: Kevin McCrimmon
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17A15

Retrieve articles in all journals with MSC: 17A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0308217-4
Keywords: Quadratic Jordan algebra, invertible element, nilpotent element
Article copyright: © Copyright 1972 American Mathematical Society