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Types of associativity inherited by a ring from a special ideal. (English) Zbl 0246.17001
MSC:
17A05 Power-associative rings
17A20 Flexible algebras
17A30 Nonassociative algebras satisfying other identities
17A15 Noncommutative Jordan algebras
17D05 Alternative rings
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References:
[1] A.A. Albert , On nonassociative division algebras , Trans. Amer. Math. Soc. 72 ( 1952 ), 296 - 309 . MR 47027 | Zbl 0046.03601 · Zbl 0046.03601 · doi:10.2307/1990756
[2] R. Block , Noncommutative Jordan algebras with commutators satisfying an alternativity condition , Proc. Nat. Acad. Sci. USA . Zbl 0208.04002 · Zbl 0208.04002 · doi:10.1073/pnas.65.1.10
[3] E.C. Johnsen , D.L. Outcalt , and Adil Yaqub , A generalization of a Theorem of Albert on finite division rings , J. Algebra 14 ( 1970 ), 106 - 111 . MR 252456 | Zbl 0198.35502 · Zbl 0198.35502 · doi:10.1016/0021-8693(70)90137-7
[4] E. Kleinfeld , M. Humm Kleinfeld , and F. Kosier , A generalization of commutative and alternative, rings , Canad. J. Math. 21 ( 1969 ), 348362 . Zbl 0198.35503 · Zbl 0198.35503 · doi:10.4153/CJM-1970-043-7
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