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On Herstein’s theorems relating Jordan and associative algebras. (English) Zbl 0224.16027


MSC:

16W10 Rings with involution; Lie, Jordan and other nonassociative structures
17A15 Noncommutative Jordan algebras
16N20 Jacobson radical, quasimultiplication
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References:

[1] McCrimmon, K., A general theory of Jordan rings, (Proc. Nat. Acad. Sci. U.S.A., 56 (1966)), 1072-1079 · Zbl 0139.25502
[2] McCrimmon, K., The radical of a Jordan algebra, (Proc. Nat. Acad. Sci. U.S.A., 59 (1969)), 671-678 · Zbl 0175.31002
[3] Herstein, I. N., On the Lie and Jordan rings of a simple associative ring, Am. J. Math., 77, 279-285 (1955) · Zbl 0064.03601
[4] Herstein, I. N., Lie and Jordan systems in simple rings with involution, Am. J. Math., 78, 629-649 (1956) · Zbl 0071.25901
[5] Herstein, I. N., Topics in Ring Theory, U. of Chicago Lecture notes (1965) · Zbl 0232.16001
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