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Identities of a finite Cayley-Dickson algebra. (English. Russian original) Zbl 0598.17013

Algebra Logic 23, 282-289 (1984); translation from Algebra Logika 23, No. 4, 407-418 (1984).
In this paper a unary, a binary, and a ternary polynomial are given which serve as a basis for the identities of the Cayley-Dickson algebra over a finite field. The existence of a finite basis for these identities was proved by I. V. L’vov [ibid. 17, No.3, 282-286 (1978; Zbl 0414.17009)].
Reviewer: L.Márki

MSC:

17D05 Alternative rings
16Rxx Rings with polynomial identity

Citations:

Zbl 0414.17009
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References:

[1] Denstrovskaya Tetrad [in Russian], Novosibirsk (1976).
[2] I. V. L’vov, ”On varieties generated by finite alternative rings,” Algebra Logika,17, No. 3, 282–286 (1978).
[3] K. A. Zhevlakov, A. M. Slin’ko, I. P. Shestakov, and A. I. Shirshov, Rings That Are Nearly Associative, Academic Press, New York (1982). · Zbl 0487.17001
[4] Yu. N. Mal’tsev and E. N. Kuz’min, ”A basis for identities of a second-order matrix algebra over a finite field,” Algebra Logika,17, No. 1, 28–32 (1978).
[5] I. V. L’vov, ”On varieties of associative rings. I,” Algebra Logika,12, No. 3, 269–297 (1973).
[6] H. P. Petersson, ”Borel subalgebras of alternative and Jordan algebras,” J. Algebra,16, No. 4, 541–560 (1970). · Zbl 0209.06802 · doi:10.1016/0021-8693(70)90007-4
[7] B. R. McDonald, Finite Rings with Identity, Marcel Dekker, New York (1974).
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