Weak polynomial identities and their applications

Vesselin Drensky

Communications in Mathematics (2021)

  • Volume: 29, Issue: 2, page 291-324
  • ISSN: 1804-1388

Abstract

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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 , ... , x n ) 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.

How to cite

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Drensky, Vesselin. "Weak polynomial identities and their applications." Communications in Mathematics 29.2 (2021): 291-324. <http://eudml.org/doc/298233>.

@article{Drensky2021,
abstract = {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.},
author = {Drensky, Vesselin},
journal = {Communications in Mathematics},
keywords = {weak polynomial identities; L-varieties; algebras with polynomial identities; central polynomials; finite basis property; Specht problem},
language = {eng},
number = {2},
pages = {291-324},
publisher = {University of Ostrava},
title = {Weak polynomial identities and their applications},
url = {http://eudml.org/doc/298233},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Drensky, Vesselin
TI - Weak polynomial identities and their applications
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 2
SP - 291
EP - 324
AB - 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.
LA - eng
KW - weak polynomial identities; L-varieties; algebras with polynomial identities; central polynomials; finite basis property; Specht problem
UR - http://eudml.org/doc/298233
ER -

References

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