The radical of the differential ideal generated by $XY$ in the ring of two variable differential polynomials is not differentially finitely generated

2019 ◽  
Vol 11 (2) ◽  
pp. 155-162
Author(s):  
David Bourqui ◽  
Julien Sebag
Keyword(s):  
Differential Polynomials ◽  
Finitely Generated ◽  
Differential Ideal

scholarly journals Multivariable dimension polynomials and new invariants of differential field extensions

2001 ◽  
Vol 27 (4) ◽  
pp. 201-214 ◽  
Author(s):  
Alexander B. Levin
Keyword(s):  
Field Extension ◽  
Differential Polynomials ◽  
Finitely Generated ◽  
Field Extensions ◽  
Differential Field ◽  
Differential Dimension ◽  
Characteristic Sets ◽  
Differential Dimension Polynomial ◽  
Dimension Polynomial

We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin's theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension.

scholarly journals Unmixed-dimensional Decomposition of a Finitely Generated Perfect Differential Ideal

2001 ◽  
Vol 31 (6) ◽  
pp. 631-649 ◽  
Author(s):  
Driss Bouziane ◽  
Abdelilah Kandri Rody ◽  
Hamid Maârouf
Keyword(s):  
Finitely Generated ◽  
Differential Ideal ◽  
Dimensional Decomposition

Computing Characteristic Sets of Ordinary Radical Differential Ideals

2006 ◽  
Vol 13 (3) ◽  
pp. 515-527
Author(s):  
Brahim Sadik
Keyword(s):  
Upper Bounds ◽  
Algebraic Methods ◽  
Characteristic Set ◽  
Finitely Generated ◽  
Differential Ideal ◽  
Characteristic Sets

Abstract We give upper bounds for the order of the elements in a characteristic set of a regular differential ideal or a radical of a finitely generated differential ideal with respect to some specific orderings. We then show how to compute characteristic sets of these ideals using algebraic methods.

Automorphisms of finite order of nilpotent groups II

2014 ◽  
Vol 51 (4) ◽  
pp. 547-555 ◽  
Author(s):  
B. Wehrfritz
Keyword(s):  
Nilpotent Group ◽  
Finite Order ◽  
Finite Index ◽  
Nilpotent Groups ◽  
Finitely Generated

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

Collectives of Automata in Finitely Generated Groups

2020 ◽  
Vol 108 (5-6) ◽  
pp. 671-678
Author(s):  
D. V. Gusev ◽  
I. A. Ivanov-Pogodaev ◽  
A. Ya. Kanel-Belov
Keyword(s):  
Finitely Generated ◽  
Finitely Generated Groups

scholarly journals TEST IDEALS IN RINGS WITH FINITELY GENERATED ANTI-CANONICAL ALGEBRAS – CORRIGENDUM

2016 ◽  
Vol 17 (4) ◽  
pp. 979-980
Author(s):  
Alberto Chiecchio ◽  
Florian Enescu ◽  
Lance Edward Miller ◽  
Karl Schwede
Keyword(s):  
Finitely Generated

Primitivity in representations of polycyclic groups

1980 ◽  
Vol 88 (1) ◽  
pp. 15-31 ◽  
Author(s):  
D. L. Harper
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Nilpotent Group ◽  
Infinite Dimension ◽  
Finitely Generated ◽  
Polycyclic Groups

In an earlier paper (5) we showed that a finitely generated nilpotent group which is not abelian-by-finite has a primitive irreducible representation of infinite dimension over any non-absolute field. Here we are concerned primarily with the converse question: Suppose that G is a polycyclic-by-finite group with such a representation, then what can be said about G?

Sign in / Sign up

Export Citation Format

Share Document