Author: Theodorus Hermanus Maria SmitsPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Skew Polynomial Rings Ans Nilpotent Derivations
Author: Theodorus Hermanus Maria SmitsPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Skew Polynomial Rings and Nilpotent Derivations
Author: Theodorus Hermanus Maria SmitsPublisher:
ISBN:
Category : Rings (Algebra)
Languages : en
Pages : 80
Book Description
Skew Polynomial Rings and Nilpotent Derivations. Proefschrift, Etc
Author: Theodorus Hermanus Maria SMITSPublisher:
ISBN:
Category :
Languages : en
Pages : 61
Book Description
Locally Nilpotent Derivations on Polynomial Rings in Two Variables Over a Field of Characteristic Zero
Author: Samuel Aristide Nyobe LikengPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The main goal of this thesis is to present the theory of Locally Nilpotent Derivations and to show how it can be used to investigate the structure of the polynomial ring in two variables k[X;Y] over a field k of characteristic zero. The thesis gives a com- plete proof of Rentschler's Theorem, which describes all locally nilpotent derivations of k[X;Y]. Then we present Rentschler's proof of Jung's Theorem, which partially describes the group of automorphisms of k[X;Y]. Finally, we present the proof of the Structure Theorem for the group of automorphisms of k[X;Y].
Locally Nilpotent Derivations of Polynomial Rings
Author: Zhiqing WangPublisher:
ISBN:
Category : Nilpotent Lie groups
Languages : en
Pages : 0
Book Description
Prime Ideals in Skew and $q$-Skew Polynomial Rings
Author: K. R. GoodearlPublisher: American Mathematical Soc.
ISBN: 0821825836
Category : Mathematics
Languages : en
Pages : 118
Book Description
New methods are developed to describe prime ideals in skew polynomial rings [italic capital]S = [italic capital]R[[italic]y; [lowercase Greek]Tau, [lowercase Greek]Delta]], for automorphisms [lowercase Greek]Tau and [lowercase Greek]Tau-derivations [lowercase Greek]Delta] of a noetherian coefficient ring [italic capital]R.
Derivations and Skew Polynomial Rings
Author: Michael G. VoskoglouPublisher:
ISBN:
Category :
Languages : en
Pages : 180
Book Description
Algebraic Theory of Locally Nilpotent Derivations
Author: Gene FreudenburgPublisher: Springer Science & Business Media
ISBN: 3540295232
Category : Mathematics
Languages : en
Pages : 266
Book Description
This book explores the theory and application of locally nilpotent derivations. It provides a unified treatment of the subject, beginning with sixteen First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings. The book also includes a wealth of pexamples and open problems.
Tackling Problems on Affine Space with Locally Nilpotent Derivations on Polynomial Rings
Author: Petrus Johannes Bernardus van RossumPublisher:
ISBN: 9789090151434
Category : Geometry, Affine
Languages : en
Pages : 132
Book Description
Prime Ideals in Skew and $Q$-Skew Polynomial Rings
Author: K. R. GoodearlPublisher: Oxford University Press, USA
ISBN: 9781470400989
Category : MATHEMATICS
Languages : en
Pages : 118
Book Description
There has been continued interest in skew polynomial rings and related constructions since Ore's initial studies in the 1930s. New examples not covered by previous analyses have arisen in the current study of quantum groups. The aim of this work is to introduce and develop new techniques for understanding the prime ideals in skew polynomial rings $S=R[y;\tau, \delta]$, for automorphisms $\tau$ and $\tau$-derivations $\delta$ of a noetherian coefficient ring $R$. Goodearl and Letzter give particular emphasis to the use of recently developed techniques from the theory of noncommutative noetherian rings. When $R$ is an algebra over a field $k$ on which $\tau$ and $\delta$ act trivially, a complete description of the prime ideals of $S$ is given under the additional assumption that $\tau -1 \delta \tau = q\delta$ for some nonzero $q\in k$. This last hypothesis is an abstraction of behavior found in many quantum algebras, including $q$-Weyl algebras and coordinate rings of quantum matrices, and specific examples along these lines are considered in detail.