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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of the elements of the socle of a Jordan algebra
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by Antonio Fernández López and Eulalia García Rus PDF
Proc. Amer. Math. Soc. 108 (1990), 69-71 Request permission

Abstract:

Let $J$ be a nondegenerate Jordan algebra over a field $K$ of characteristic not 2 . Here we prove that an element $b \in J$ is in the socle if and only if $J$ satisfies dcc on all principal inner ideals ${U_y}J,y \in Kb + {U_b}J$. By using this result we show that the socle of a quadratic extension ${J_F}$ of $J$ coincides with the quadratic extension ${\text {Soc(}}J{)_F}$ of its socle.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 69-71
  • MSC: Primary 17C10; Secondary 16A34, 17C65
  • DOI: https://doi.org/10.1090/S0002-9939-1990-0991702-0
  • MathSciNet review: 991702