BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Serdica Mathematical Journal >
2012 >
Volume 38, Number 1-3 >

Please use this identifier to cite or link to this item:

Title: Asymptotic behaviour of Functional Identities
Authors: Gordienko, A. S.
Keywords: Functional Identity
Generalized Functional Identity
Amitsur’s Conjecture
Regev’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.
ISSN: 1310-6600
Appears in Collections:Volume 38, Number 1-3

Files in This Item:

File Description SizeFormat
2012-259-272.pdf495.07 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License