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Polynomial codimension growth and the Specht problem

  • Autori: Giambruno, A; Mishchenko, S; Valenti, A; Zaicev M.
  • Anno di pubblicazione: 2017
  • Tipologia: Articolo in rivista (Articolo in rivista)
  • OA Link:


We construct a continuous family of algebras over a field of characteristic zero with slow codimension growth bounded by a polynomial of degree 4. This is achieved by building, for any real number α ∈(0, 1) a commutative nonassociative algebra A_α whose codimension sequence c_n(A_α), n =1, 2, ..., is polynomially bounded . As an application we are able to construct a new example of a variety with an infinite basis of identities.