Cover Image

On the kernels of higher R-derivations of R[x1, ... xn]

Let R be an integral domain and A = R[x1, . . . , xn] be the polynomial ring in n variables. In this article, we study the kernel of higher R-derivation D of A. It is shown that if R is a HCF ring and tr. degR(Aᴰ) ≤ 1 then Aᴰ = R[f] for some f ∈ A.

Saved in:

Bibliographic Details
Published in:	Algebra and Discrete Mathematics
Date:	2021
Main Author:	Kour, S.
Format:	Article
Language:	English
Published:	Інститут прикладної математики і механіки НАН України 2021
Online Access:	https://nasplib.isofts.kiev.ua/handle/123456789/188750
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:	On the kernels of higher R-derivations of R[x1, ... xn] / S. Kour // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 236-240. — Бібліогр.: 9 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine

Similar Items

Dynamical behavior of rational difference equation xn+1=(xn−13)/(±1± xn−1xn−3xn−5xn−7xn−9xn−11xn−13)
by: D. Şimşek, et al.
Published: (2024)

On the recursive sequence x(n+1)=xn-(k+1)/1+xnxn-1...xn-k
by: Simsek, D., et al.
Published: (2017)

On the recursive sequence x(n+1)=xn-(k+1)/1+xnxn-1...xn-k
by: D. Şimşek, et al.
Published: (2017)

A Note on the Recursive Sequence xn+1=pkxn+pk−1xn−1+...+p1xn−k+1
by: Stevic, S.
Published: (2003)

Резонансно-туннельные диоды на основе нитридов AlN/AlxGa1-xN, GaN/InxGa1-xN
by: Боцула, О.В., et al.
Published: (2008)

Approximation of the $| x |^r$ function and its derivatives
by: Shvai, A. I., et al.
Published: (1990)

Recombination and long-term relaxation of photoconductivity in r+–r–r– structures of CdxHg1–xTe (0.24 ≤ x ≤ 0.29)
by: N. J. Ismayilov, et al.
Published: (2018)

Коли R(X) і R⟨X⟩ є ω-евклідовими областями
by: Sagan, A. V.; Саган А. В.; Львівський національний університет ім. Івана Франка, Львів
Published: (2018)

The interaction of the components in the R2T2In1-xGax (R = La, Ce; T = Ni, Cu) systems
by: N. Dominiuk, et al.
Published: (2022)

On Pointwise Estimates for Convex Polynomial Approximation of Function with Fractional Derivatives of Arbitrary Order r &gt; 4, r ie R
by: T. O. Petrova, et al.
Published: (2017)

On the dependence of the norm of a function on the norms of its derivatives of orders $k$ , $r - 2$ and $r , 0 < k < r - 2$
by: Babenko, V. F., et al.
Published: (2012)

The RCuIn1–xGax (R = La, Ce) systems at 870 K
by: N. Zaremba, et al.
Published: (2021)

BestL1-approximations of classes $W_1^r$ by Splines from $W_1^r$
by: Babenko, V. F., et al.
Published: (1994)

Atomistic models for R1-xPrxBa2Cu3O7-δ (R = Y and lanthanides) and related oxides
by: A. I. Chroneos, et al.
Published: (2009)

Synthesis and antiviral activity of [(9-R1-10-R2-3-R-2-oxo-2H-[1,2,4]-triazino[2,3-s]quinazolin-6-yl)thio]acetamides derivatives with the fragments of carcass amines
by: I. S. Nosulenko, et al.
Published: (2014)

When R(X) and $RX $ are ω-Euclidean domains
by: A. V. Sahan
Published: (2018)

Приближение функции |x|r и ее производных
by: Швай, А.И., et al.
Published: (1990)

Антипроліферативна дія нових похідних 1-(4-R-бензил)-3-R1-4-(R2-феніламіно)-1Н-пірол-2,5-діону
by: Дубініна, Г.Г., et al.
Published: (2007)

Method of comparison for differential equations with the Hukuhara derivative in the space conv(R
by: E. V. Ocheretnjuk, et al.
Published: (2014)

Циклоконденсації 3-(R²-аміно)-3-метилтіо-1-R¹-пропенонів з 2-аміноазолами
by: Брицун, В.М., et al.
Published: (2008)

Kernels of derivations of polynomial rings and Casimir elements
by: Bedratyuk, L. P., et al.
Published: (2010)

Estimates of the area of solutions of the pseudolinear differential equations with Hukuhara derivative in the space (R
by: E. V. Ocheretnjuk, et al.
Published: (2017)

The synthesis of 3-methyl-6-r-|1,2,4|triazolo|3,4-b|-|1,3,4|-thiadiazole derivatives
by: T. V. Hlazunova, et al.
Published: (2020)

Approximative characteristics of the Nikol’skii – Besov classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$
by: Radchenko, O. Ya., et al.
Published: (2026)

The synthesis of 4-thiazolidinone derivatives using 2-(4-R-2-formylphenoxy)-N-(R&#039;-phenyl)acetamides and their anti-inflammatory activity
by: S. M. Golota, et al.
Published: (2015)

The synthesis and the study of antimicrobial properties of 5-R,R&#039;-aminometylene derivatives of thiazolidine-2,4-dione and 4-thioxothiazolidine-2-one
by: G. O. Derkach, et al.
Published: (2016)

Semi-free R1 action and Bott map
by: V. Sharko, et al.
Published: (2013)

Studying the Currency Risk: the Conceptions of VaR and CFaR
by: A. I. Bondarenko
Published: (2016)

Топологічна класифікація афінних відображень з R² в R²
by: Будницька, Т.В.
Published: (2008)

Скрещенные групповые кольца с условием тривиальности решений уравнения xⁿ - μ = 0
by: Баранник, А.Ф., et al.
Published: (1983)

Synthesis and physicochemical properties of derivatives of 7-R-3-benzylxanthinyl-8-methylthioacetic acid
by: K. V. Aleksandrova, et al.
Published: (2013)

The search for substances with the antimicrobial activity among morpholine-containing 2-R-phenyliminothiazole derivatives
by: H. O. Yeromina, et al.
Published: (2019)

Polymorphism in the short arm of 1R rye chromosomes in wheat lines with 1RS.1BL translocation and 1R(1B) substitution from different sources
by: M. K. Toporash, et al.
Published: (2018)

Умови оборотності нелінійного різницевого оператора (Dx)(n) = x(n+1) - f(x(n)) у просторі l∞(Z, R)
by: Слюсарчук, В.Ю.
Published: (2006)

Generalized higher derivations on algebras
by: A. Foљner
Published: (2017)

Generalized higher derivations on algebras
by: Fošner, A., et al.
Published: (2017)

Genre Peculiarities of J. R. R. Tolkien&#039;s Fantasy
by: N. Sytnyk
Published: (2009)

The bidual of r-algebras
by: Yilmaz, R.
Published: (2011)

The bidual of r-algebras
by: Yilmaz, R., et al.
Published: (2011)

An elementary description of \(K_1(R)\) without elementary matrices
by: Hüttemann, T., et al.
Published: (2020)