# GALOIS GROUPS OF MODULES AND INVERSE POLYNOMIAL MODULES

• Park, Sang-Won ;
• Jeong, Jin-Sun
• Published : 2007.05.31
• 66 6

#### Abstract

Given an injective envelope E of a left R-module M, there is an associative Galois group Gal$({\phi})$. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope $E[x^{-1}]$ of an inverse polynomial module $M[x^{-1}]$ as a left R[x]-module and we can define an associative Galois group Gal$({\phi}[x^{-1}])$. In this paper we describe the relations between Gal$({\phi})$ and Gal$({\phi}[x^{-1}])$. Then we extend the Galois group of inverse polynomial module and can get Gal$({\phi}[x^{-s}])$, where S is a submonoid of $\mathbb{N}$ (the set of all natural numbers).

#### Keywords

injective module;injective envelope;Galois group;inverse polynomial module

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#### Cited by

1. Generalized Inverse Power Series Modules vol.39, pp.8, 2011, https://doi.org/10.1080/00927872.2010.491101