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Weak polynomial identities and their applications

Vesselin Drensky * 
* Corresponding author
Abstract : Let R be an associative algebra over a field K generated by a vector subspace V. The polynomial f(x 1, . . . , xn ) of the free associative algebra K〈x 1, x 2, . . .〉 is a weak polynomial identity for the pair (R, V) if it vanishes in R when evaluated on V. We survey results on weak polynomial identities and on their applications to polynomial identities and central polynomials of associative and close to them nonassociative algebras and on the finite basis problem. We also present results on weak polynomial identities of degree three.
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Submitted on : Wednesday, May 11, 2022 - 1:51:10 PM
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Vesselin Drensky. Weak polynomial identities and their applications. Communications in Mathematics, 2021, Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in Málaga) (2), pp.291 - 324. ⟨10.2478/cm-2021-0022⟩. ⟨hal-03665023⟩

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