eng
episciences.org
Communications in Mathematics
1804-1388
2336-1298
2021-07-15
Volume 29 (2021), Issue 2...
10.2478/cm-2021-0022
9541
journal article
Weak polynomial identities and their applications
Vesselin Drensky
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.
https://cm.episciences.org/9541/pdf
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