Shestakov, I. P. Associative identities of octonions. (English. Russian original) Zbl 1248.17002 Algebra Logic 49, No. 6, 561-565 (2011); translation from Algebra Logika 49, No. 6, 834-839 (2010). Summary: We work to find a basis of identities for an octonion algebra modulo an associator ideal of a free alternative algebra, or, in other words, a basis for an associative replica of an ideal of identities of an octonion algebra. Cited in 2 Documents MSC: 17A30 Nonassociative algebras satisfying other identities 17D05 Alternative rings Keywords:octonion algebra; Cayley-Dickson algebra; basis of identities × Cite Format Result Cite Review PDF Full Text: DOI References: [1] J. N. Conway and D. A. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry, A. K. Peters, Natick, MA (2003). · Zbl 1098.17001 [2] J. C. Baez, ”The octonions,” Bull. Am. Math. Soc., New Ser., 39, No. 2, 145–205 (2002); · Zbl 1026.17001 · doi:10.1090/S0273-0979-01-00934-X [3] J. C. Baez, ”Errata,” Bull. Am. Math. Soc., New Ser., 42, 213 (2005). · doi:10.1090/S0273-0979-05-01043-8 [4] I. P. Shestakov, ”Radicals and nilpotent elements of free alternative algebras,” Algebra Logika, 14, No. 3, 354–365 (1975). · Zbl 0351.17016 · doi:10.1007/BF01668557 [5] K. A. Zhevlakov, A. M. Slin’ko, I. P. Shestakov, and A. I. Shirshov, Rings That Are Nearly Associative [in Russian], Nauka, Moscow (1978). · Zbl 0445.17001 [6] I. M. Isaev, ”Identities of a finite Cayley–Dickson algebra,” Algebra Logika, 23, No. 4, 407–418 (1984). · Zbl 0598.17013 · doi:10.1007/BF02071788 [7] A. V. Il’tyakov, ”The Specht property of ideals of identities of certain simple nonassociative algebras,” Algebra Logika, 24, No. 3, 327–351 (1985). · Zbl 0615.03036 · doi:10.1007/BF01978708 [8] M. L. Racine, ”Minimal identities of octonion algebras,” J. Alg., 115, No. 1, 251–260 (1988). · Zbl 0651.17012 · doi:10.1016/0021-8693(88)90294-3 [9] I. R. Hentzel and L. A. Peresi, ”Identities of Cayley–Dickson algebras,” J. Alg., 188, No. 1, 292–309 (1997). · Zbl 0890.17001 · doi:10.1006/jabr.1996.6814 [10] I. Shestakov and N. Zhukavets, ”Skew-symmetric identities of octonions,” J. Pure Appl. Alg., 213, No. 4, 479–492 (2009). · Zbl 1241.17033 · doi:10.1016/j.jpaa.2008.07.012 [11] Yu. P. Razmyslov, ”The existence of a finite basis of identities for a matrix algebra of second order over a field of characteristic 0,” Algebra Logika, 12, No. 1, 81–113 (1973). · Zbl 0282.17003 · doi:10.1007/BF02218641 [12] V. C. Drensky, ”A minimal basis of identities for a second-order matrix algebra over a field of characteristic zero,” Algebra Logika, 20, No. 3, 282–290 (1981). · Zbl 0635.03035 · doi:10.1007/BF01669112 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.