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Simple right alternative rings. (English. Russian original) Zbl 0401.17009

Algebra Logic 16, 456-476 (1978); translation from Algebra Logika 16, 682-710 (1977).

MSC:

17D05 Alternative rings
17D99 Other nonassociative rings and algebras
Full Text: DOI

References:

[1] Dnestr Notebook, Unsolved Problems of the Theory of Rings and Modules [in Russian], Novosibirsk (1976).
[2] K. A. Zhevlakov, ”Solvability of alternative nil rings,” Sib. Mat. Zh.,3, No. 3, 368–377 (1962). · Zbl 0139.03401
[3] K. A. Zhevlakov, ”Remarks on simple alternative rings,” Algebra Logika,6, No. 2, 21–33 (1967).
[4] K. A. Zhevlakov, A. M. Slin’ko, I. P. Shestakov, and A. I. Shirshov, Alternative Algebras [in Russian], Vol. 1, Novosibirsk (1976). · Zbl 0402.17018
[5] I. M. Mikheev, ”The locally right nilpotent radical in the class of right alternative rings,” Algebra Logika,11, No. 2, 174–185 (1972).
[6] R. É Roomel’di, ”Solvability of (,1) nil rings,” Algebra Logika,12, No. 4, 478–489 (1973).
[7] A. I. Shirshov, ”On certain nonassociative nil rings and algebraic algebras,” Mat. Sb.,41, No. 3, 381–394 (1957). · Zbl 0078.02202
[8] I. R. Hentzel, ”Right alternative rings,” Doctoral Dissertation, Univ. Iowa (1968); Diss. Abst.,B29, No. 11 (1969), 4267.
[9] I. R. Hentzel, ”Right alternative rings with idempotents,” J. Algebra,17, 303–309 (1971). · Zbl 0218.17011 · doi:10.1016/0021-8693(71)90012-3
[10] I. N. Herstein, ”On the Lie and Jordan rings of a simple associative ring,” Am. J. Math.,77, 279–285 (1955). · Zbl 0064.03601 · doi:10.2307/2372531
[11] E. Kleinfeld, ”On right alternative rings without proper right ideals,” Pac. J. Math.,31, No. 1, 87–102 (1969). · Zbl 0186.06704
[12] A. Thedy, ”Right alternative rings,” J. Algebra,37, No. 1, 1–43 (1975). · Zbl 0318.17011 · doi:10.1016/0021-8693(75)90086-1
[13] A. Thedy, ”Right alternative rings with Peirce decomposition,” J. Algebra,37, No. 1, 44–63 (1975). · Zbl 0318.17012 · doi:10.1016/0021-8693(75)90087-3
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