Перегляд за автором "Petravchuk, A.P."

Сортувати за: Порядок: Результатів:

  • Closed polynomials and saturated subalgebras of polynomial algebras 
    Arzhantsev, I.V.; Petravchuk, A.P. (Український математичний журнал, 2007)
    The behavior of closed polynomials, i.e., polynomials f∈k[x₁,…,xn]∖k such that the subalgebra k[f] is integrally closed in k[x₁,…,xn], is studied under extensions of the ground field. Using some properties of closed ...
  • Finite-dimensional subalgebras in polynomial Lie algebras of rank one 
    Arzhantsev, I.V.; Makedonskii, E.A.; Petravchuk, A.P. (Український математичний журнал, 2011)
    Let Wn(K) be the Lie algebra of derivations of the polynomial algebra K[X] := K[x1, . . . , xn] over an algebraically closed field K of characteristic zero. A subalgebra L ⊆ Wn(K) is called polynomial if it is a submodule ...
  • On closed rational functions in several variables 
    Petravchuk, A.P.; Iena, O.G. (Algebra and Discrete Mathematics, 2007)
    Let K = K¯ be a field of characteristic zero. An element ϕ ∈ K(x1,... ,xn) is called a closed rational function if the subfield K(ϕ) is algebraically closed in the field K(x1,... ,xn). We prove that a rational function ...
  • On nilpotent Lie algebras of derivations of fraction fields 
    Petravchuk, A.P. (Algebra and Discrete Mathematics, 2016)
  • On one-sided Lie nilpotent ideals of associative rings 
    Luchko, V.S.; Petravchuk, A.P. (Algebra and Discrete Mathematics, 2007)
    We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of ...
  • To the Fiftieth Anniversary of the Department of Algebra and Mathematical Logic of Kyiv Taras Shevchenko University 
    Bezushchak, O.O.; Drozd, Yu.A.; Gorodniy, M.F.; Petravchuk, A.P.; Sushchanskiy, V.I. (Algebra and Discrete Mathematics, 2010)
    History of algebraic research in Kyiv University starts in 1902 when Professor D. Grave who was a pupil of the St.Petersburg mathematical school started his work at Kyiv University. After moving to Kyiv Professor Grave ...