Goldie Extending Modules |
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Authors: | Evrim Akalan Adnan Tercan |
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Affiliation: | Department of Mathematics , Hacettepe University , Beytepe Campus, Ankara, Turkey |
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Abstract: | In this article, we define a module M to be 𝒢-extending if and only if for each X ≤ M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We consider the decomposition theory for 𝒢-extending modules and give a characterization of the Abelian groups which are 𝒢-extending. In contrast to the charac-terization of extending Abelian groups, we obtain that all finitely generated Abelian groups are 𝒢-extending. We prove that a minimal cogenerator for 𝒢od-R is 𝒢-extending, but not, in general, extending. It is also shown that if M is (𝒢-) extending, then so is its rational hull. Examples are provided to illustrate and delimit the theory. |
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Keywords: | C 11-module C 11-ring Extending module FI-extending module Rational hull Uniform module |
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