Middle nucleus=center in semiprime Jordan algebras
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- by Kevin McCrimmon and Seong Nam Ng PDF
- Proc. Amer. Math. Soc. 86 (1982), 21-24 Request permission
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
- A. A. Albert, On the nuclei of a simple Jordan algebra, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 446–447. MR 153718, DOI 10.1073/pnas.50.3.446
- Nathan Jacobson, Structure theory of Jordan algebras, University of Arkansas Lecture Notes in Mathematics, vol. 5, University of Arkansas, Fayetteville, Ark., 1981. MR 634508
- Erwin Kleinfeld, Middle nucleus-center in a simple Jordan ring, J. Algebra 1 (1964), 40–42. MR 161893, DOI 10.1016/0021-8693(64)90005-5
- E. I. Zel′manov, Jordan division algebras, Algebra i Logika 18 (1979), no. 3, 286–310, 385 (Russian). MR 566787
- Seong Nam Ng, Middle nucleus of semiprime Jordan rings, Nanta Math. 9 (1976), no. 1, 1–3. MR 466238
Additional Information
- © Copyright 1982 American Mathematical Society
- 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