Abstract
In this paper, we will study the irreducibility of the discrete Painlevé equation of type D7(1) in the sense of decomposable extensions. The irreducibility here particularly implies that the transcendental function solution cannot be built from rational functions by reiterating algebraic operations, the taking of a solution of a linear difference equation and the taking of a solution of a first-order algebraic difference equation. We also study non-existence of algebraic function solution. A modification to the definition of the decomposable extension is mentioned.
