Non-Linear Algebraic Difference Equations with Formal Solutions of the Same Type as the Formal Solutions of Linear Homogeneous Difference Equations

1939 ◽  
Vol 61 (1) ◽  
pp. 187
Author(s):  
Otis E. Lancaster
Keyword(s):  
Difference Equations ◽  
Non Linear ◽  
Algebraic Difference ◽  
Formal Solutions

scholarly journals Finiteness Properties of Affine Difference Algebraic Groups

2020 ◽  
Author(s):  
Michael Wibmer
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Difference Equations ◽  
General Linear Group ◽  
Algebraic Groups ◽  
The Matrix ◽  
Algebraic Difference ◽  
The Difference ◽  
Linear Differential ◽  
Finiteness Properties

Abstract We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the matrix entries can indeed be defined by finitely many such equations. As an application, we show that the difference ideal of all difference algebraic relations among the solutions of a linear differential equation is finitely generated.

Sign in / Sign up

Export Citation Format

Share Document