In this work is proved, that anyone anticommutative Engel algebra G is nilpotent, if dim K G ≤ 4. And on the contrary, if n = dim K G > 4, then for anyone n there is example solvable Engel algebra,… Expand

Two necessary and sufficient criteria for the simultaneous triangulability of two complex matrices are established. Both of them admit a finite verification procedure. To prove the first criterion,… Expand

In this paper, we study some properties of algebras of associative type introduced in previous papers of the author. We show that a finite-dimensional algebra of associative type over a field of zero… Expand

In this paper, we describe finite-dimensional homogeneously simple algebras of associative type whose 1-component is a full matrix algebra. In addition, we prove that a finite-dimensional division… Expand

Lie type algebras introduced in [1], [2] are natural generalizations of Lie algebras, associative algebras, Lie superalgebras with Z2-grading, and of algebras of some other classes. In [3], we… Expand