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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...
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