We study central polynomials of a relatively free Lie nilpotent algebra $ F^{(n)} $ of degree $
n $. We prove a product theorem, which generalizes the well-known results of Latyshev and …

Изучаются центральные многочлены относительно свободной лиево нильпотентной
степени n алгебры F (n). Доказана теорема о произведении, обобщающая известные …

Let Z< X> be the free unital associative ring freely generated by an infinite countable set
X={x 1, x 2,…}. Define a left-normed commutator [x 1, x 2,…, xn] by [a, b]= ab− ba,[a, b, c]=[[a …

Consider the free algebra An generated over Q by n generators x1,…, xn. Interesting objects
attached to A= An are members of its lower central series, Li= Li (A), defined inductively by …

The paper naturally continues series of works on identical relations of group rings,
enveloping algebras, and other related algebraic structures. Let L be a Lie algebra over a …

Let F be a field and let F< X> be the free unital associative algebra over F freely generated
by an infinite countable set X={x 1, x 2,…}. Define a left-normed commutator [a 1, a 2,…, an] …

The lower central series invariants M k of an associative algebra A are the two-sided ideals
generated by k-fold iterated commutators; the M k provide a filtration of A. We study the …

In this article, we mainly study the products of commutator ideals of Lie-admissible algebras
such as Novikov algebras, bicommutative algebras, and assosymmetric algebras. More …

Let A be a unital associative ring and let T (k) be the two-sided ideal of A generated by all
commutators [a 1, a 2,…, ak](ai∈ A) where [a 1, a 2]= a 1 a 2− a 2 a 1,[a 1,…, ak− 1, ak]=[[a …

Let Z< X> be the free unital associative ring freely generated by an infinite countable set
X={x 1, x 2,…}. Define a left-normed commutator [a 1, a 2,…, an] inductively by [a, b]= ab …