Geodesic
Asymptotic behaviour of Functional Identities
Serdica Mathematical Journal, Tome 38 (2012) no. 1-3, pp. 259-272.

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We calculate the asymptotics of functional codimensions fcn(A) and generalized functional codimensions gfc n (A) of an arbitrary not necessarily associative algebra A over a field F of any characteristic. Namely, fcn(A) ∼ gfcn(A) ∼ dim(A^2) · (dim A^n) as n → ∞ for any finite-dimensional algebra A. In particular, codimensions of functional and generalized functional identities satisfy the analogs of Amitsur’s and Regev’s conjectures. Also we precisely evaluate fcn(UT2(F)) = gfcn(UT2(F)) = 3^(n+1) − 2^(n+1).
Keywords: Functional Identity, Generalized Functional Identity, Codimension, Growth, Algebra, Amitsur’s Conjecture, Regev’s Conjecture 
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Gordienko, A. S. Asymptotic behaviour of Functional Identities. Serdica Mathematical Journal, Tome 38 (2012) no. 1-3, pp. 259-272. http://geodesic.mathdoc.fr/item/SMJ2_2012_38_1-3_a12/