Výsledky vyhledávání - "DERYABINA, GALINA"

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On some products of commutators in an associative ring

Autor: Deryabina, Galina, Krasilnikov, Alexei

Publikováno v: International Journal of Algebra and Computation 29 (2019) 333-341

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 $[a_1, a_2] = a_1 a_2 - a_2 a_1$, $[a_1, \dots , a_{k-1}, a_k] = \bigl[ [a_1, \dots , a_{k

Externí odkaz: http://arxiv.org/abs/1812.03585

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Products of several commutators in a Lie nilpotent associative algebra

Autor: Deryabina, Galina, Krasilnikov, Alexei

Publikováno v: International Journal of Algebra and Computation, 27 (2017), 1027-1040

Let $F$ be a field of characteristic $\ne 2,3$ 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 by $[a_1, a_2] = a_1 a_2 - a_2 a_1$, $[a_1, \dots , a_{n-1}, a_n] = [[

Externí odkaz: http://arxiv.org/abs/1610.03136

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Products of commutators in a Lie nilpotent associative algebra

Autor: Deryabina, Galina, Krasilnikov, Alexei

Publikováno v: Journal of Algebra 469 (2017) 84 - 95

Let $F$ be a field and let $F \langle X \rangle$ be the free unital associative algebra over $F$ freely generated by an infinite countable set $X = \{x_1, x_2, \dots \}$. Define a left-normed commutator $[a_1, a_2, \dots, a_n]$ recursively by $[a_1,

Externí odkaz: http://arxiv.org/abs/1509.08890

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The subalgebra of graded central polynomials of an associative algebra

Autor: Deryabina, Galina, Krasilnikov, Alexei

Publikováno v: Journal of Algebra 425 (2015) 313-323

Let $F$ be a field and let $F \langle X \rangle$ be the free unital associative $F$-algebra on the free generating set $X = \{ x_1, x_2, \dots \}$. A subalgebra (a vector subspace) $V$ in $F \langle X \rangle$ is called a $T$-subalgebra (a $T$-subspa

Externí odkaz: http://arxiv.org/abs/1409.7937

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

Autor: Deryabina, Galina, Krasilnikov, Alexei

Publikováno v: Journal of Algebra 428 (2015) 230-255

Let $\mathbb Z \langle X \rangle$ be the free unital associative ring freely generated by an infinite countable set $X = \{ x_1,x_2, \dots \}$. Define a left-normed commutator $[x_1,x_2, \dots, x_n]$ by $[a,b] = ab - ba$, $[a,b,c] = [[a,b],c]$. For $

Externí odkaz: http://arxiv.org/abs/1308.4172

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

Autor: Deryabina, Galina, Krasilnikov, Alexei

Publikováno v: Journal of Algebra 519 (2019) 101-110

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 proved that if [R] is a nilpotent Lie ring of class c then U(R) is a nil

Externí odkaz: http://arxiv.org/abs/1305.1350

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