Geodesic
On the Relationship between the Length of an Algebra and the Index of Nilpotency of Its Jacobson Radical
Matematičeskie zametki, Tome 94 (2013) no. 5, pp. 682-688

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

A sharp upper bound for the length of an algebra as a function of the index of nilpotency of its Jacobson radical and the length of the quotient algebra by the radical is obtained.
Keywords: algebra over a field, length of an algebra, index of nilpotency, Jacobson radical, ideal.
Mots-clés : quotient algebra, subalgebra 
O. V. Markova. On the Relationship between the Length of an Algebra and the Index of Nilpotency of Its Jacobson Radical. Matematičeskie zametki, Tome 94 (2013) no. 5, pp. 682-688. http://geodesic.mathdoc.fr/item/MZM_2013_94_5_a3/
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[1] R. Pirs, Assotsiativnye algebry, Mir, M., 1986 | MR | Zbl

[2] Ch. J. Pappacena, “An upper bound for the length of a finite-dimensional algebra”, J. Algebra, 197:2 (1997), 535–545 | DOI | MR | Zbl

[3] O. V. Markova, “Verkhnyaya otsenka dliny kommutativnykh algebr”, Matem. sb., 200:12 (2009), 41–62 | DOI | MR | Zbl

[4] D. Constantine, M. Darnall, “Lengths of finite dimensional representations of PWB algebras”, Linear Algebra Appl., 395 (2005), 175–181 | DOI | MR | Zbl

[5] O. V. Markova, “O nekotorykh svoistvakh funktsii dliny”, Matem. zametki, 87:1 (2010), 83–91 | DOI | MR | Zbl

[6] A. E. Guterman, O. V. Markova, “Commutative matrix subalgebras and length function”, Linear Algebra Appl., 430:7 (2009), 1790–1805 | DOI | MR | Zbl

[7] O. V. Markova, “Vychislenie dlin matrichnykh podalgebr spetsialnogo vida”, Fundament. i prikl. matem., 13:4 (2007), 165–197 | MR | Zbl

[8] R. Lidl, G. Niderraiter, Konechnye polya, T. 1, 2, Mir, M., 1988 | MR | MR | Zbl