Bulletin of the Korean Mathematical Society (대한수학회보)

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GALOIS GROUPS OF MODULES AND INVERSE POLYNOMIAL MODULES

  • Published : 2007.05.31
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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).

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References

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