Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2797

 Title: Asymptotic behaviour of Functional Identities Authors: Gordienko, A. S. Keywords: Functional IdentityGeneralized Functional IdentityCodimensionGrowthAlgebraAmitsur’s ConjectureRegev’s Conjecture Issue Date: 2012 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 38, No 1-3, (2012), 259p-272p Abstract: 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). Description: 2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69. URI: http://hdl.handle.net/10525/2797 ISSN: 1310-6600 Appears in Collections: Volume 38, Number 1-3

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