Geodesic
Nil Ideals of Finite Codimension in Alternative Noetherian Algebras
Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 395-402.

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Alternative (right) Noetherian algebras are considered. It is proved that, in these algebras, the nil ideals of finite codimension are nilpotent, which generalizes the corresponding Zhevlakov's result. As a corollary, we describe just infinite alternative nonassociative algebras (for the field characteristic distinct from 2).
Keywords: Noetheriaty, nil ideal, alternative algebra, just infinite algebra, exceptional algebra, codimension. 
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V. N. Zhelyabin; A. S. Panasenko. Nil Ideals of Finite Codimension in Alternative Noetherian Algebras. Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 395-402. http://geodesic.mathdoc.fr/item/MZM_2017_101_3_a5/

[1] J. Levitzki, “On multiplicative systems”, Compositio Math., 8 (1950), 76–80 | MR | Zbl

[2] K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov, A. I. Shirshov, Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl

[3] K. A. Zhevlakov, “Zamechaniya o lokalno nilpotentnykh koltsakh s usloviyami obryva”, Matem. zametki, 12:2 (1972), 121–126 | MR | Zbl

[4] A. S. Panasenko, “Pochti konechnomernye alternativnye algebry”, Matem. zametki, 98:5 (2015), 747–755 | DOI | MR | Zbl

[5] S. V. Pchelintsev, “Isklyuchitelnye pervichnye alternativnye algebry”, Sib. matem. zhurn., 48:6 (2007), 1322–1337 | MR | Zbl

[6] S. V. Pchelintsev, “Pervichnye alternativnye algebry, blizkie k kommutativnym”, Izv. RAN. Ser. matem., 68:1 (2004), 183–206 | DOI | MR | Zbl

[7] J. Farina, C. Pendergrass-Rice, “A few properties of just infinite algebras”, Comm. Algebra, 35:5 (2007), 1703–1707 | MR | Zbl