Geodesic
Algebraic algebras and prime varieties of associative algebras
Sbornik. Mathematics, Tome 200 (2009) no. 5, pp. 723-751 Cet article a éte moissonné depuis la source Math-Net.Ru

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The following problem of Kemer is solved for prime varieties of associative algebras with unit: it is shown that over an infinite field of positive characteristic, each prime variety of associative algebras with unit is generated by an algebraic algebra of bounded algebraicity index over this field. Bibliography: 10 titles.
Keywords: polynomial identities, varieties of algebras
Mots-clés : algebraic algebras. 
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L. M. Samoilov. Algebraic algebras and prime varieties of associative algebras. Sbornik. Mathematics, Tome 200 (2009) no. 5, pp. 723-751. http://geodesic.mathdoc.fr/item/SM_2009_200_5_a5/

[1] A. Kemer, “PI-algebras and nil algebras of bounded index”, Trends in ring theory (Miscolc, Hungary, 1996), CMS Conf. Proc., 22, Amer. Math. Soc., Providence, RI, 1998, 59–69 | MR | Zbl

[2] A. R. Kemer, Ideals of identities of associative algebras, Transl. Math. Monogr., 87, Amer. Math. Soc., Providence, RI, 1991 | MR | Zbl

[3] I. Sviridova, “Varieties and algebraic algebras of bounded degree”, J. Pure Appl. Algebra, 133:1–2 (1998), 233–240 | DOI | MR | Zbl

[4] I. Yu. Sviridova, “T-pervichnye mnogoobraziya i algebraicheskie algebry”, Fundament. i prikl. matem., 8:1 (2002), 221–243 | MR | Zbl

[5] L. M. Samoilov, “On the nilindex of the radical of a relatively free associative algebra”, Math. Notes, 82:3–4 (2007), 522–530 | DOI | MR | Zbl

[6] L. M. Samoǐlov, “Radical of a relatively free associative algebra over fields of positive characteristic”, Sb. Math., 199:5 (2008), 707–753 | DOI | MR | Zbl

[7] L. M. Samoilov, “Analog teoremy Levitskogo dlya beskonechno porozhdennykh assotsiativnykh algebr”, Mat. zametki (to appear)

[8] A. R. Kemer, “Representability of reduced free algebras”, Algebra and Logic, 27:3 (1988), 167–184 | DOI | MR | Zbl

[9] A. R. Kemer, “Identities of finitely generated algebras over an infinite field”, Math. USSR-Izv., 37:1 (1991), 69–96 | DOI | MR | Zbl

[10] A. R. Kemer, “Finite basis property of identities of associative algebras”, Algebra and Logic, 26:5 (1987), 362–397 | DOI | MR | Zbl | Zbl