Jordan rings with involution
HTML articles powered by AMS MathViewer
- by Seong Nam Ng PDF
- Trans. Amer. Math. Soc. 200 (1974), 111-139 Request permission
Abstract:
Let $J$ be a Jordan ring with involution $\ast$ in which $2x = 0$ implies $x = 0$ and in which $2J = J$. Let the set $S$ of symmetric elements of $J$ be periodic and let $N$ be the Jacobson radical of $J$. Then ${N^2} = 0$ and $J/N$ is a subdirect sum of $\ast$-simple Jordan rings of the following types (1) a periodic field, (2) a direct sum of two simple periodic Jordan rings with exchange involution, (3) a $3 \times 3$ or $4 \times 4$ Jordan matrix algebra over a periodic field, (4) a Jordan algebra of a nondegenerate symmetric bilinear form on a vector space over a periodic field.References
-
D. J. Britten Goldie-like conditions on Jordan matrix rings, Ph. D. Thesis, University of Iowa, Iowa City, 1971.
- Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099
- Kevin McCrimmon, A general theory of Jordan rings, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 1072–1079. MR 202783, DOI 10.1073/pnas.56.4.1072
- Kevin McCrimmon, The radical of a Jordan algebra, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 671–678. MR 268238, DOI 10.1073/pnas.62.3.671
- Kevin McCrimmon, A characterization of the radical of a Jordan algebra, J. Algebra 18 (1971), 103–111. MR 277583, DOI 10.1016/0021-8693(71)90129-3
- Susan Montgomery, A generalization of a theorem of Jacobson, Proc. Amer. Math. Soc. 28 (1971), 366–370. MR 276272, DOI 10.1090/S0002-9939-1971-0276272-5
- 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
- J. Marshall Osborn, Jordan and associative rings with nilpotent and invertible elements, J. Algebra 15 (1970), 301–308. MR 262316, DOI 10.1016/0021-8693(70)90058-X
- J. Marshall Osborn, Varieties of algebras, Advances in Math. 8 (1972), 163–369 (1972). MR 289587, DOI 10.1016/0001-8708(72)90003-5
- Chester Tsai, The prime radical in a Jordan ring, Proc. Amer. Math. Soc. 19 (1968), 1171–1175. MR 230776, DOI 10.1090/S0002-9939-1968-0230776-X
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 200 (1974), 111-139
- MSC: Primary 17C10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0399198-2
- MathSciNet review: 0399198