# Asymptotic behaviour of Functional Identities

Serdica Mathematical Journal (2012)

- Volume: 38, Issue: 1-3, page 259-272
- ISSN: 1310-6600

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topGordienko, A. S.. "Asymptotic behaviour of Functional Identities." Serdica Mathematical Journal 38.1-3 (2012): 259-272. <http://eudml.org/doc/288278>.

@article{Gordienko2012,

abstract = {2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69.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).* Supported by post doctoral fellowship from Atlantic Association for Research in Mathematical Sciences (AARMS), Atlantic Algebra Centre (AAC), Memorial University of Newfoundland (MUN), and Natural Sciences and Engineering Research Council of Canada (NSERC).},

author = {Gordienko, A. S.},

journal = {Serdica Mathematical Journal},

keywords = {Functional Identity; Generalized Functional Identity; Codimension; Growth; Algebra; Amitsur’s Conjecture; Regev’s Conjecture},

language = {eng},

number = {1-3},

pages = {259-272},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Asymptotic behaviour of Functional Identities},

url = {http://eudml.org/doc/288278},

volume = {38},

year = {2012},

}

TY - JOUR

AU - Gordienko, A. S.

TI - Asymptotic behaviour of Functional Identities

JO - Serdica Mathematical Journal

PY - 2012

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 38

IS - 1-3

SP - 259

EP - 272

AB - 2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69.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).* Supported by post doctoral fellowship from Atlantic Association for Research in Mathematical Sciences (AARMS), Atlantic Algebra Centre (AAC), Memorial University of Newfoundland (MUN), and Natural Sciences and Engineering Research Council of Canada (NSERC).

LA - eng

KW - Functional Identity; Generalized Functional Identity; Codimension; Growth; Algebra; Amitsur’s Conjecture; Regev’s Conjecture

UR - http://eudml.org/doc/288278

ER -

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