Jordan algebras with minimum condition
HTML articles powered by AMS MathViewer
- by David L. Morgan PDF
- Trans. Amer. Math. Soc. 155 (1971), 161-173 Request permission
Abstract:
Let $J$ be a Jordan algebra with minimum condition on quadratic ideals over a field of characteristic not 2. We construct a maximal nil ideal $R$ of $J$ such that $J/R$ is a direct sum of a finite number of ideals each of which is a simple Jordan algebra. $R$ must have finite dimension if it is nilpotent and this is shown to be the case whenever $J$ has “enough” connected primitive orthogonal idempotents.References
- A. A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc. 69 (1950), 503–527. MR 38959, DOI 10.1090/S0002-9947-1950-0038959-X
- N. Jacobson, Structure theory for a class of Jordan algebras, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 243–251. MR 193116, DOI 10.1073/pnas.55.2.243
- N. Jacobson, A coordinatization theorem for Jordan algebras, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 1154–1160. MR 140553, DOI 10.1073/pnas.48.7.1154
- J. Marshall Osborn, Jordan algebras of capacity two, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 582–588. MR 215892, DOI 10.1073/pnas.57.3.582
- Richard D. Schafer, An introduction to nonassociative algebras, Pure and Applied Mathematics, Vol. 22, Academic Press, New York-London, 1966. MR 0210757 M. B. Slater, The Wedderburn-Artin theorem for alternative rings, Notices Amer. Math. Soc. 15 (1968), 382. Abstract #68T-277.
- M. F. Smiley, The radical of an alternative ring, Ann. of Math. (2) 49 (1948), 702–709. MR 25449, DOI 10.2307/1969053
- K. A. Ževlakov, On radical ideals of an alternative ring, Algebra i Logika Sem. 4 (1965), no. 4, 87–102 (Russian). MR 0194485
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 155 (1971), 161-173
- MSC: Primary 17.40
- DOI: https://doi.org/10.1090/S0002-9947-1971-0276290-1
- MathSciNet review: 0276290