10 citations · 12 across the 3 of their papers we have counts for
3 papers
math.RA2008
On behavior of solvable ideals of Lie algebras under outer derivations
Anatoliy P. Petravchuk
Let be a finite dimensional Lie algebra over a field . It is well known that the solvable radical of the algebra is a characteristic ideal of if $\char F=0$ a…
math.RA2008★ 2 cited
On one-sided Lie nilpotent ideals of associative rings
V. S. Luchko, A. P. Petravchuk
We prove that a Lie nilpotent one-sided ideal of an associative ring is contained in a Lie solvable two-sided ideal of . An estimation of derived length of such Lie solvable…
math.RA2007★ 10 cited
On closed rational functions in several variables
A. P. Petravchuk, O. G. Iena
Let k be an algebraically closed field of characteristic zero. An element F from k(x_1,...,x_n) is called a closed rational function if the subfield k(F) is algebraically closed in…