Right representations of algebras. (English. Russian original) Zbl 0342.17003
Algebra Logic 13(1974), 312-333 (1975); translation from Algebra Logika 13, 544-588 (1974).
MSC:
| 17A99 | General nonassociative rings |
| 17A65 | Radical theory (nonassociative rings and algebras) |
| 17D15 | Right alternative rings |
Citations:
Zbl 0262.17010References:
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| [2] | K. A. Zhevlakov, ?Remarks about simple alternative rings,? Algebra i Logika,6, No. 2, 21-34 (1967). |
| [3] | K. A. Zhevlakov, ?Identity of Smiley and Kleinfeld radicals in alternative rings,? Algebra i Logika,8, No. 3, 309-319 (1969). |
| [4] | K. A. Zhevlakov, ?Quasiregular ideals in finitely generated alternative rings,? Algebra i Logika,11, No. 2, 140-161 (1972). · Zbl 0262.17009 |
| [5] | K. A. Zhevlakov, ?Radical and representations of alternative rings,? Algebra i Logika,11, No. 2, 162-173 (1972). · Zbl 0262.17010 |
| [6] | A. I. Mal’tsev, Algebraic Systems [in Russian], Moscow (1970). |
| [7] | V. T. Markov, ?On the dimension of noncommutative affine algebras,? IAN SSSR, Ser. Matem.,37, No. 2, 284-288 (1973). · Zbl 0255.16007 |
| [8] | A. M. Slin’ko, ?Radicals of Jordan rings related to alternative rings,? Matem. Zametki,16, No. 1, 135-140 (1974). |
| [9] | A. I. Shirshov, ?Nonassociative nil-rings and algebraic algebras,? Mat. Sb.,41, 381-394 (1957). · Zbl 0078.02202 |
| [10] | A. A. Albert, ?The structure of right-alternative algebras,? Ann. Math.,59, No. 3, 408-417 (1954). · Zbl 0055.26501 · doi:10.2307/1969709 |
| [11] | R. H. Bruck and E. Kleinfeld, ?The structure of alternative division rings,? Proc. Amer. Math. Soc.,2, No. 6, 878-890 (1951). · Zbl 0044.02205 · doi:10.1090/S0002-9939-1951-0045099-9 |
| [12] | S. Eilenberg, ?Extensions of general algebras,? Ann. Soc. Polon. Math.,21, 125-134 (1948). · Zbl 0031.34303 |
| [13] | I. N. Herstein, ?On the Lie and Jordan rings of a simple associative ring,? Amer. J. Math.,77, 279-285 (1955). · Zbl 0064.03601 · doi:10.2307/2372531 |
| [14] | N. Jacobson, ?Structure of alternative and Jordan bimodules,? Osaka J. Math.,6, 1-71 (1954). · Zbl 0059.02902 |
| [15] | N. Jacobson, ?Structure and representations of Jordan algebras,? Amer. Math. Soc. Coll. Publ.,39 (1968). · Zbl 0218.17010 |
| [16] | N. Jacobson and C. E. Rickart, ?Jordan homomorphisms of rings,? Trans. Amer. Math. Soc.,69, 479-502 (1950). · Zbl 0039.26402 |
| [17] | E. Kleinfeld, ?Right-alternative rings,? Proc. Amer. Math. Soc.,4, 939-944 (1953). · Zbl 0052.26703 · doi:10.1090/S0002-9939-1953-0059888-X |
| [18] | E. Kleinfeld, ?Simple alternative rings,? Ann. Math.,58, 544-547 (1953). · Zbl 0051.02503 · doi:10.2307/1969753 |
| [19] | E. Kleinfeld, ?Primitive alternative rings and semisimplicity,? Amer. J. Math.,77, 725-730 (1955). · Zbl 0066.02302 · doi:10.2307/2372593 |
| [20] | J. M. Osborn, ?Representations and radicals of Jordan algebras,? Scr. Math.,29, Nos. 3-4, 297-329 (1973). · Zbl 0264.17006 |
| [21] | R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York (1966). · Zbl 0145.25601 |
| [22] | M. Slater, ?Nucleus and center in alternative rings,? J. of Algebra,7, 372-388 (1967). · Zbl 0166.30402 · doi:10.1016/0021-8693(67)90077-4 |
| [23] | M. Slater, ?Prime alternative rings I and II,? J. of Algebra,15, 229-250 (1970). · Zbl 0193.34304 · doi:10.1016/0021-8693(70)90075-X |
| [24] | M. F. Smiley, ?The radical of alternative rings,? Ann. of Math.,49, No. 3, 702-709 (1948). · Zbl 0031.34501 · doi:10.2307/1969053 |
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