GALOIS GROUPS OF MODULES AND INVERSE POLYNOMIAL MODULES

Title & Authors
GALOIS GROUPS OF MODULES AND INVERSE POLYNOMIAL MODULES
Park, Sang-Won; Jeong, Jin-Sun;

Abstract
Given an injective envelope E of a left R-module M, there is an associative Galois group Gal$\small{({\phi})}$. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope $\small{E[x^{-1}]}$ of an inverse polynomial module $\small{M[x^{-1}]}$ as a left R[x]-module and we can define an associative Galois group Gal$\small{({\phi}[x^{-1}])}$. In this paper we describe the relations between Gal$\small{({\phi})}$ and Gal$\small{({\phi}[x^{-1}])}$. Then we extend the Galois group of inverse polynomial module and can get Gal$\small{({\phi}[x^{-s}])}$, where S is a submonoid of $\small{\mathbb{N}}$ (the set of all natural numbers).
Keywords
injective module;injective envelope;Galois group;inverse polynomial module;
Language
English
Cited by
1.
Generalized Inverse Power Series Modules, Communications in Algebra, 2011, 39, 8, 2779
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