Geodesic
Just Infinite Alternative Algebras
Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 747-755.

Voir la notice de l'article provenant de la source Math-Net.Ru

Alternative just infinite-dimensional algebras are studied, i.e., infinite-dimensional algebras in which every nonzero ideal has finite codimension. It is proved that these algebras are prime. In the nonassociative case, the Noetherian property with respect to one-sided ideals is proved, and the cases of Cayley–Dickson rings and exceptional algebras are investigated.
Keywords: alternative algebra, just infinite-dimensional algebra, prime algebra, Noetherian property with respect to one-sided ideals, Cayley–Dickson ring, exceptional algebra. 
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A. S. Panasenko. Just Infinite Alternative Algebras. Matematičeskie zametki, Tome 98 (2015) no. 5, pp. 747-755. http://geodesic.mathdoc.fr/item/MZM_2015_98_5_a7/

[1] A. Shalev, E. I. Zelmanov, “Narrow Lie algebras: a coclass theory and a characterization of the Witt algebra”, J. Algebra, 189:2 (1997), 294–331 | DOI | MR | Zbl

[2] D. R. Farkas, L. W. Small, “Algebras which are nearly finite dimensional and their identities”, Israel J. Math, 127 (2002), 245–251 | DOI | MR | Zbl

[3] Z. Reichstein, D. Rogalski, J. J. Zhang, “Projectively simple rings”, Adv. Math., 203:2 (2006), 365–407 | DOI | MR | Zbl

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

[5] A. Anquela, T. Cortés, F. Montaner, “Nonassociative coalgebras”, Comm. Algebra, 22:12 (1994), 4693–4716 | DOI | MR | Zbl

[6] V. N. Zhelyabin, “Strukturizuemye koalgebry”, Algebra i logika, 35:5 (1996), 529–542 | MR | Zbl

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

[8] I. P. Shestakov, “Absolyutnye deliteli nulya i radikaly konechno-porozhdennykh alternativnykh algebr”, Algebra i logika, 15:5 (1976), 585–602 | MR | Zbl

[9] R. D. Schafer, An Introduction to Nonassociative Algebras, Pure Appl. Math., 22, Academic Press, New York, 1966 | MR | Zbl

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

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

[12] I. Kherstein, Nekommutativnye koltsa, Mir, M., 1972 | MR | Zbl