Given an injective envelope E of a left R-module M, there is an associative Galois group Gal. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope of an inverse polynomial module as a left R[x]-module and we can define an associative Galois group Gal. In this paper we describe the relations between Gal and Gal. Then we extend the Galois group of inverse polynomial module and can get Gal, where S is a submonoid of (the set of all natural numbers).