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
Author(s):  
Michael Wibmer

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.


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