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About Nilpotency of Engel Algebras
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
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On the Simultaneous Triangulability of Matrices
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
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Modules and ideals of algebras of associative type
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 zeroExpand
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Triangulation of n-tuple solvable Lie algebras
We prove an analog of the Lie theorem for finite-dimensional n-tuple solvable Lie algebras over an algebraically closed field of characteristic 0.
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Finite-dimensional homogeneously simple algebras of associative type
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 divisionExpand
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Symmetrical simple Lie sheaves of rank 1
In terms of sandwich algebras, we obtain a classification of symmetrical simple Lie sheaves over an algebraically closed field of zero characteristic.
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Cartan Subalgebras with Engel Decomposition
A class of algebras of associative type
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], weExpand
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