Prime radicals of special Lie superalgebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 51-60.

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The concept of a generally special Lie superalgebra was introduced. It was proved that the locally solvable graded radical of a generally special Lie superalgebra coincides with its prime graded radical.
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I. N. Balaba; S. A. Pikhtilkov. Prime radicals of special Lie superalgebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 51-60. http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a3/

[1] Bakhturin Yu. A., Mikhalev A. A., Petrogradskij V. M., Zajtsev M. V., Infinite dimensional Lie superalgebras, De Gruyter Expositions in Mathematics, 7, 1992 | MR | Zbl

[2] Latyshev V. N., “Ob algebrakh Li s tozhdestvennymi sootnosheniyami”, Sib. mat. zhurnal, 4:4 (1963), 821–829 | Zbl

[3] Bergen J., Cohen M., “Action of Commutative Hopf Algebras”, Bull. Lond. Math. Soc., 18 (1986), 159–164 | DOI | MR | Zbl

[4] Bahturin Yu., Giambruno A., Riley D., “Group-graded algebras with polynomial identity”, Israel J. Math., 104 (1998), 145–155 | DOI | MR | Zbl

[5] Bahturin Yu., Montgomery S., “PI-envelopes of Lie syperalgebras”, Proc. Amer. Math. Soc., 127:10 (1999), 2829–2939 | DOI | MR

[6] Pikhtilkov S. A., “O spetsialnykh algebrakh Li”, Uspekhi mat. nauk, 36:6 (1981), 225–226 | MR

[7] Bahturin Yu., “On Lie subalgebras of associative PI-algebras”, J. Algebra, 67:2 (1980), 257–271 | DOI | MR | Zbl

[8] Nǎstǎsescu C., Van Oystayen F., Graded Ring Theory, North-Holland, Amsterdam, 1982 | MR

[9] Beidar K. I., Pikhtilkov S. A., “Pervichnyi radikal spetsialnykh algebr Li”, Fundam. i prikl. mat., 6:3 (2000), 643–648 | MR | Zbl

[10] Scheunert M., The Theory of Lie Superalgebras, Lect. Notes in Math., 716, 1979 | MR | Zbl

[11] Cohen M., Montgomery S., “Group-graded rings, smash products, and group action”, Trans. Amer. Math. Soc., 282:1 (1984), 237–258 ; addendum Trans. Amer. Math. Soc., 300:2 (1987), 810–811 | DOI | MR | Zbl | DOI | MR | Zbl

[12] Andrunakievich V. A., Ryabukhin Yu. M., Radikaly algebr i strukturnaya teoriya, Nauka, M., 1979 | MR

[13] Regev A., “Existence of identities in $A\otimes_F B$”, Israel J. Math., 11:2 (1972), 131–152 | DOI | MR | Zbl

[14] Lin Shaoxue, Beattie M., Fang Hangjin, “Graded division rings and the Jacobson density theorem”, J. of Beijing Normal University (Natural Science), 27:2 (1991), 129–134 | MR

[15] Zhu, Bin, “Graded primitive rings and Kaplansky's theorem”, Beijing Shifan Daxue Xuebao, 34:1 (1988), 1–5 | MR

[16] Balaba I. N., Graduirovannye pervichnye PI-algebry (to appear)

[17] Razmyslov Yu. P., “O radikale Dzhekobsona v PI-algebrakh”, Algebra i logika, 13:3 (1974), 337–360 | MR | Zbl

[18] Kemer A. R., “Tozhdestva Kapelli i nilpotentnost radikala konechno porozhdennoi PI-algebry”, DAN SSSR, 245:4 (1980), 793–797 | MR

[19] Braun A., “The nilpotency of the radical in a finitely generated PI-ring”, J. Algebra, 89:2 (1984), 375–396 | DOI | MR | Zbl