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pro vyhledávání: '"Petravchuk, Anatoliy"'
Let $K$ be a field, $R=K[x, y]$ the polynomial ring and $\mathcal{M}(K)$ the set of all pairs of square matrices of the same size over $K.$ Pairs $P_1=(A_1,B_1)$ and $P_2=(A_2,B_2)$ from $\mathcal{M}(K)$ are called similar if $A_2=X^{-1}A_1X$ and $B_
Externí odkaz:
http://arxiv.org/abs/2408.04244
We prove analogs of A.~Selberg's result for finitely generated subgroups of $\text{Aut}(A)$ and of Engel's theorem for subalgebras of $\text{Der}(A)$ for a finitely generated associative commutative algebra $A$ over an associative commutative ring. W
Externí odkaz:
http://arxiv.org/abs/2211.10781
Publikováno v:
In Linear Algebra and Its Applications 1 May 2019 568:165-172
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as subalgebras of
Externí odkaz:
http://arxiv.org/abs/1211.4165
Autor:
Petravchuk, Anatoliy P.
Let $k$ be an arbitrary field of characteristic zero, $k[x, y]$ be the polynomial ring and $D$ a $k$-derivation of the ring $k[x, y]$. Recall that a nonconstant polynomial $F\in k[x, y]$ is said to be a Darboux polynomial of the derivation $D$ if $D(
Externí odkaz:
http://arxiv.org/abs/0911.2073
Autor:
Petravchuk, Anatoliy P.
Let $L$ be a finite dimensional Lie algebra over a field $F$. It is well known that the solvable radical $S(L)$ of the algebra $L$ is a characteristic ideal of $L$ if $\char F=0$ and there are counterexamples to this statement in case $\char F=p>0$.
Externí odkaz:
http://arxiv.org/abs/0808.3262
Publikováno v:
Mat. Zametki 86:5 (2009), 659--663; transl. in Math. Notes 86 (2009), no. 5, 625--628
Every subfield $\kk(\phi)$ of the field of rational functions $\kk(x_1,...,x_n)$ is contained in a unique maximal subfield of the form $\kk(\psi)$. The element $\psi$ is called generative for the element $\phi$. A subfield of $\kk(x_1,...,x_n)$ is ca
Externí odkaz:
http://arxiv.org/abs/0808.3132
Publikováno v:
Ukrain. Mat. Zh. 59:12 (2007), 1587--1593; transl. in Ukrainian Math. J. 59:12 (2007), 1783--1790
New and old results on closed polynomials, i.e., such polynomials f in K[x_1,...,x_n] that the subalgebra K[f] is integrally closed in K[x_1,...,x_n], are collected. Using some properties of closed polynomials we prove the following factorization the
Externí odkaz:
http://arxiv.org/abs/math/0608157
Publikováno v:
Transactions of the American Mathematical Society; Feb2024, Vol. 377 Issue 2, p1335-1356, 22p
Autor:
Petravchuk, Anatoliy P.
Publikováno v:
In Linear Algebra and Its Applications 2010 433(3):574-579