Goldie extending modules and generalizations of quasi-continuous modules. (Q407369)
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scientific article; zbMATH DE number 6336990
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Goldie extending modules and generalizations of quasi-continuous modules. |
scientific article; zbMATH DE number 6336990 |
Statements
Goldie extending modules and generalizations of quasi-continuous modules. (English)
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1 September 2014
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A module \(M\) is called GQC (generalized quasi-continuous) if for every submodules \(X_1\) and \(X_2\) with \(X_1\cap X_2=0\) there exist an essential submodule \(X'_i\) of \(X_i\) and a decomposition \(M=A_1\oplus A_2\) such that \(X'_i\) is a submodule of \(A_i\) (\(i=1,2\)). The author studies GQC-modules, including direct sums, direct summands and relationship with some generalization of the extending property.
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Goldie extending modules
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quasi-continuous modules
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ejective modules
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direct sums
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direct summands
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extending property
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finite internal exchange property
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