The ideal of identities of a variety generated by n-dimensional 2-algebras
Year: 2025
Type: article
Abstract: The problems related to the description of identities that hold in all n-dimensional associative nilpotent algebras over a field (n is fixed) are studied. The author previously formulated the hypothesis that an arbitrary n-dimensional nilpotent algebra over any field satisfies some standard identity of minimal degree, and a number of results were obtained in support of this hypothesis. In this article, it turns out that this hypothesis is also confirmed in the class of 2-algebras, that is, such locally nilpotent algebras over a field that the square of the principal ideal generated by any of the generators of the algebra is equal to zero. Moreover, the ideal of identities of a variety generated by n-dimensional 2-algebras over an arbitrary field (n is fixed) is described.
Source: Russian Mathematics
Author: E. P. Petrov
Institution: Altai State University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4408008413