A. Krasilnikov

activity

20122026

most citedThe additive group of a Lie nilpotent associative ring

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

collaborators

Showing 2013Show all

4 papers · 1 filter

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…

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

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