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Middle nucleus=center in semiprime Jordan algebras


Authors: Kevin McCrimmon and Seong Nam Ng
Journal: Proc. Amer. Math. Soc. 86 (1982), 21-24
MSC: Primary 17C10
DOI: https://doi.org/10.1090/S0002-9939-1982-0663858-6
MathSciNet review: 663858
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Abstract: A. A. Albert showed that the middle nucleus and center coincide for a simple Jordan algebra finite-dimensional over a field of characteristic $ \ne 2$. E. Kleinfeld extended this to arbitrary simple Jordan algebras of characteristic $ \ne 2$. Recently this result has played a crucial role in the structure theory of E. Zelmanov. In this note we extend the result to linear Jordan algebras with no derivation-invariant trivial ideals.


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

  • [1] A. A. Albert, On the nuclei of a simple Jordan algebra, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 446-447. MR 0153718 (27:3679)
  • [2] N. Jacobson, Structure theory of Jordan algebras, University of Arkansas Lecture Notes, Fayetteville, 1981. MR 634508 (83b:17015)
  • [3] E. Kleinfeld, Middle nucleus$ {}={}$center in a simple Jordan ring, J. Algebra 1 (1964), 40-42. MR 0161893 (28:5097)
  • [4] E. I. Zelmanov, Jordan division rings, Algebra i Logika 18 (1979), 286-310. MR 566787 (81m:17021)
  • [5] Ng Seong Nam, Middle nucleus of semiprime Jordan rings, Nanta Mathematica 9 (1976), 1-3. MR 0466238 (57:6118)

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DOI: https://doi.org/10.1090/S0002-9939-1982-0663858-6
Article copyright: © Copyright 1982 American Mathematical Society

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