Isaev, I. M. 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 Cited in 5 Documents MSC: 17D05 Alternative rings 16Rxx Rings with polynomial identity Keywords:generators; identities; Cayley-Dickson algebra; finite field Citations:Zbl 0414.17009 × Cite Format Result Cite Review PDF Full Text: DOI EuDML 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). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.