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 manifold generated by \(n\) -dimensional 2-algebras over an arbitrary field ( \(n\) is fixed) is described.
