A. Krasilnikov

activity

20122018

most citedThe additive group of a Lie nilpotent associative ring

16 citations · 50 across the 11 of their papers we have counts for

collaborators

11 papers

math.RA2018★ 4 cited

On some products of commutators in an associative ring

Galina Deryabina, Alexei Krasilnikov

Let $A$ be a unital associative ring and let $T^{(k)}$ be the two-sided ideal of $A$ generated by all commutators $[a_{1}, a_{2}, \dots, a_{k}]$ $(a_{i} \in A)$ where $[a_1, a_2] = a_1 a_…

math.RA2017

On Lie nilpotent associative algebras

Claud W. G. Dias, Alexei Krasilnikov

Let $G$ be a group generated by a set $X$ . It is well known and easy to check that \[ [g_1, g_2, \dots ,g_n] = 1 \mbox{ for all } g_i \in G \qquad \iff \qquad [x_1, x_2, \dots , x_…

math.RA2016★ 1 cited

Products of several commutators in a Lie nilpotent associative algebra

Galina Deryabina, Alexei Krasilnikov

Let $F$ be a field of characteristic $\neq = 2, 3$ and let $A$ be a unital associative $F$ -algebra. Define a left-normed commutator $[a_{1}, a_{2}, \dots, a_{n}]$ $(a_{i} \in A)$ recursively…

math.RA2015★ 9 cited

Products of commutators in a Lie nilpotent associative algebra

Galina Deryabina, Alexei Krasilnikov

Let $F$ be a field and let $F ⟨ X ⟩$ be the free unital associative algebra over $F$ freely generated by an infinite countable set $X = {x_{1}, x_{2}, \dots}$ . Define a…

math.RA2014★ 1 cited

The subalgebra of graded central polynomials of an associative algebra

Galina Deryabina, Alexei Krasilnikov

Let $F$ be a field and let $F ⟨ X ⟩$ be the free unital associative $F$ -algebra on the free generating set $X = {x_{1}, x_{2}, \dots}$ . A subalgebra (a vector subspace)…

math.RA2013

Symmetric polynomials and non-finitely generated $S y m (N)$ -invariant ideals

Eudes Antonio da Costa, Alexei Krasilnikov

Let $K$ be a field and let $N = {1, 2, \dots}$ . Let $R_{n} = K [x_{ij} ∣ 1 \leq i \leq n, j \in N]$ be the ring of polynomials in $x_{ij}$ $(1 \le i \le n, j \in \mathbb…

math.RA2013★ 9 cited

The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3

Galina Deryabina, Alexei Krasilnikov

Let $Z ⟨ X ⟩$ be the free unital associative ring freely generated by an infinite countable set $X = {x_{1}, x_{2}, \dots}$ . Define a left-normed commutator $[x_…

math.RA2013★ 8 cited

Relations in universal Lie nilpotent associative algebras of class 4

Eudes Antonio da Costa, Alexei Krasilnikov

Let $K$ be a unital associative and commutative ring and let $K ⟨ X ⟩$ be the free unital associative $K$ -algebra on a non-empty set $X$ of free generators. Define a le…

math.RA2013

A 5-Engel associative algebra whose group of units is not 5-Engel

Galina Deryabina, Alexei Krasilnikov

Let R be an associative ring with unity and let [R] and U(R) denote the associated Lie ring (with [a,b]=ab-ba) and the group of units of R, respectively. In 1983 Gupta and Levin pr…

math.RA2012★ 2 cited

Limit T-subspaces and the central polynomials in n variables of the Grassmann algebra

Dimas José Gonçalves, Alexei Krasilnikov, Irina Sviridova

Let F<X> be the free unitary associative algebra over a field F on the set X = {x_1, x_2, ...}. A vector subspace V of F<X> is called a T-subspace (or a T-space) if V is closed und…

math.RA2012★ 16 cited

The additive group of a Lie nilpotent associative ring

Alexei Krasilnikov

Let Z<X> be the free unitary associative ring freely generated by an infinite countable set X = {x_1, x_2,...}. Define a left-normed commutator [x_1, x_2, ..., x_n] by [a,b] = ab -…

On some products of commutators in an associative ring

On Lie nilpotent associative algebras

Products of several commutators in a Lie nilpotent associative algebra

Products of commutators in a Lie nilpotent associative algebra

The subalgebra of graded central polynomials of an associative algebra

Symmetric polynomials and non-finitely generated Sym(N)-invariant ideals

The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3

Relations in universal Lie nilpotent associative algebras of class 4

A 5-Engel associative algebra whose group of units is not 5-Engel

Limit T-subspaces and the central polynomials in n variables of the Grassmann algebra

The additive group of a Lie nilpotent associative ring

Symmetric polynomials and non-finitely generated $S y m (N)$ -invariant ideals