A. Krasilnikov

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2 papers · 1 filter

math.RA2018

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_…