Literature cited
N. Jacobson, Structure and Representations of Jordan Algebras, Amer. Math. Soc. Colloq. Publ.,39, Providence (1968).
A. M. Slin'ko, "The Jacobson radical and absolute zero divisors in special Jordan algebras," Algebra Logika,11, No. 6, 711–723 (1972).
I. M. Mikheev, "Simple right-alternative rings," Algebra Logika,16, No. 3, 682–710 (1977).
K. McCrimmon, "Absolute zero divisors and local nilpotency in alternative algebras," Proc. Am. Math. Soc.,47, No. 2, 293–299 (1975).
I. P. Shestakov, "Absolute zero divisors and radicals of finitely generated alternative algebras," Algebra Logika,15, No. 5, 585–602 (1976).
S. V. Pchelintsev, "Metaideals of alternative algebras," in: Fourth All-Union Symposium on the Theory of Rings, Algebras, and Modules [in Russian], Kishinev (1980), pp. 87–88.
K. A. Zhevlakov et al., Nearly Associative Rings [in Russian], Nauka, Moscow (1978).
I. R. Hentzel, "The characterization of (−1, 1)-ring," J. Algebra,30, No. 1–3, 236–258 (1974).
C. Maueri, "Simple (−1, 1)-rings with an idempotent," Proc. Am. Math. Soc.,14, 110–117 (1963).
R. É. Roomel'di, "Solvability of (−1, 1)-nilrings," Algebra Logika,12, No. 4, 478–489 (1973).
S. V. Pchelintsev, "Nilpotence of the associator ideal of a free finitely generated (−1, 1)-ring," Algebra Logika,14, No. 5, 543–571 (1975).
M. Atiyah and I. MacDonald, Introduction to Commutative Algebra [Russian translation], Mir, Moscow (1972).
S. V. Pchelintsev, "Nilpotence of associators in a free (−1, 1)-ring," Algebra Logika,13, No. 2, 217–223 (1974).
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Translated from Algebra i Logika, Vol. 21, No. 6, pp. 706–720, November–December, 1982.
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Pchelintsev, S.V. Absolute zero divisors of special jordan algebras. Algebra and Logic 21, 470–480 (1982). https://doi.org/10.1007/BF01982208
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DOI: https://doi.org/10.1007/BF01982208