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Almost Semi-extending Modules
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Fuchs introduced purely extending modules as a generalization of extending modules. Ahmed and Abbas gave another generalization for extending modules named semi-extending modules. In this paper, two generalizations of the extending modules are combined to give another generalization. This generalization is said to be almost semi-extending. In fact, the purely extending modules lies between the extending and almost semi-extending modules. We also show that an almost semi-extending module is a proper generalization of purely extending. In addition, various examples and important properties of this class of modules are given and considered. Another characterization of almost semi-extending modules is established. Moreover, the relationships with other related concepts are studied and discussed
University of Baghdad College of Science
Title: Almost Semi-extending Modules
Description:
Fuchs introduced purely extending modules as a generalization of extending modules.
Ahmed and Abbas gave another generalization for extending modules named semi-extending modules.
In this paper, two generalizations of the extending modules are combined to give another generalization.
This generalization is said to be almost semi-extending.
In fact, the purely extending modules lies between the extending and almost semi-extending modules.
We also show that an almost semi-extending module is a proper generalization of purely extending.
In addition, various examples and important properties of this class of modules are given and considered.
Another characterization of almost semi-extending modules is established.
Moreover, the relationships with other related concepts are studied and discussed.
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