Abstract
Results in the theory of nonassociative rings and related directions reviewed in RZhMatematika during the period 1972–1978 are discussed. Special attention is given to infinite-dimensional Lie algebras, Jordan algebras, alternative rings, Mal'tsev algebras, and varieties, representations, and radicals of nonassociative rings.
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Literature cited
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B. O. Makarevich, “Ideal points of semisimple Jordan algebras,” Mat. Zametki,15, No. 2, 295–305 (1974).
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A. S. Markovichev, “Nil-systems and the radical in alternative Artinian rings,” Mat, Zametki,11, No. 3, 299–306 (1972).
A. S. Markovichev, “On the hereditary property of radicals of rings of type (γ, δ),” Algebra Logika,17, No. 1, 33–55 (1978).
A. S. Markovichev, “Nil-rings of type (γ, δ),” Algebra Logika,17, No. 2, 181–200 (1978).
A. S. Markovichev, “The lower nil-radical of rings of type (γ, δ),” Algebra Logika,17, No. 3, 287–302 (1978).
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Ya. A. Medvedev, “Local finiteness of periodic subloops of alternative PI-rings,” Mat. Sb.,103, No. 6, 309–315 (1977).
Yu. A. Medvedev, “The finite-basis property for varieties with a two-term identity,” Algebra Logika,17, No. 6, 705–726 (1978).
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Yu. A. Medvedev, “An example of a variety of solvable alternative algebras over a field of characteristic 2 which does not have a finite basis of identities,” Algebra Logika,19, No. 3, 300–313 (1980).
I. M. Mikheev, “The locally right-nilpotent radical in the class of right alternative rings,” Algebra Logika,11, No. 2, 174–185 (1972).
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I. M. Mikheev, “On prime right alternative algebras,” Algebra Logika,14, No. 1, 56–60 (1975).
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A. A. Nikitin, “Almost alternative algebras,” Algebra Logika,13, No. 5, 501–533 (1974).
A. A. Nikitin, “On the hereditary property of radicals of rings,” Algebra Logika,17, No. 3, 303–315 (1978).
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A. Yu. Ol'shanskii, “On some infinite systems of identities,” Tr. Sem. im. I. G. Petrovskogo, No. 3, 139–145 (1978).
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V. A. Parfenov, “On a property of ideals of free Lie algebras,” Sib. Mat. Zh.,12, No. 1, 171–176 (1969).
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S. V. Pchelintsev, “Nilpotence of the associator ideal of a finitely generated (−1, 1)-ring,” Algebra Logika,14, No. 5, 543–571 (1975).
S. V. Pchelintsev, “Defining identities of a variety of right alternative algebras,” Mat. Zametki,20, No. 2, 161–176 (1976).
S. V. Pchelintsev, “On a local nilpotent radical in some classes of right alternative rings,” Sib. Mat. Zh.,17, No. 2, 340–360 (1976).
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Yu. P. Razmyslov, “On an example of nonsolvable, almost Cross varieties of groups,” Algebra Logika,11, No. 2, 186–205 (1972).
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Yu. P. Razmyslov, “On a finite basis of identities of a matrix algebra of second order over a field of characteristic zero,” Algebra Logika,121, No. 1, 83–113 (1973).
Yu. P. Razmyslov, “On the Jacobson radical in PI-algebras,” Algebra Logika,13, 337–360 (1974).
Yu. P. Razmyslov, “Trace identities of complete matrix algebras over a field of characteristic 0,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 4, 723–757 (1974).
Yu. P. Razmyslov, “On the Hall-Higman problem,” Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 4, 833–847 (1978).
E. V. Ritter, “Skeletons of solvable varieties of Lie algebras,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 50–61 (1980).
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A. V. Sidorov, “On noncommutative ternary Lie algebras,” Algebr. Sistemy, Ivanovo, pp. 81–86.
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Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 18, pp 3–72 1981.
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Bakhturin, Y.A., Slin'ko, A.M. & Shestakov, I.P. Nonassociative rings. J Math Sci 18, 169–211 (1982). https://doi.org/10.1007/BF01255614
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DOI: https://doi.org/10.1007/BF01255614