Geodesic
Weak polynomial identities and their applications
Communications in Mathematics, Tome 29 (2021) no. 2, pp. 291-324.

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Let $R$ be an associative algebra over a field $K$ generated by a vector subspace $V$. The polynomial $f(x_1,\ldots ,x_n)$ of the free associative algebra $K\langle x_1,x_2,\ldots \rangle $ 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.
Classification : 16R10, 16R30, 17B01, 17B20, 17C05, 17C20, 20C30
Keywords: weak polynomial identities; L-varieties; algebras with polynomial identities; central polynomials; finite basis property; Specht problem 
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     title = {Weak polynomial identities and their applications},
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Drensky, Vesselin. Weak polynomial identities and their applications. Communications in Mathematics, Tome 29 (2021) no. 2, pp. 291-324. http://geodesic.mathdoc.fr/item/COMIM_2021__29_2_a10/