6533b7d6fe1ef96bd126670a
RESEARCH PRODUCT
Polynomial codimension growth and the Specht problem
Mikhail ZaicevAntonio GiambrunoS. MishchenkoA. Valentisubject
Discrete mathematicsPolynomialAlgebra and Number TheoryDegree (graph theory)Polynomial identity Codimension Growth010102 general mathematicsZero (complex analysis)Field (mathematics)Basis (universal algebra)Codimension01 natural sciences010101 applied mathematicsSettore MAT/02 - AlgebraBounded function0101 mathematicsVariety (universal algebra)Mathematicsdescription
Abstract 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 and lim log n c n ( A α ) = 3 + α . As an application we are able to construct a new example of a variety with an infinite basis of identities.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-01-01 |