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Uniform Purely Extending Modules | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 27, Issue 1, 2016, Pages 74-77 | ||
| Author | ||
| Saad Abdulkadhim Al-Saadi | ||
| Abstract | ||
| An R-module M is extending if every submodule of M is essential in a direct summand of M. Many generalizations of extending modules are studied. Following Clark, an R-module M is purely extending if every submodule of M is essential in a pure submodule of M. Also, an R-module M is called uniform-extending if every uniform submodule X of M is essential in a direct summand D of M. In this paper, we introduce and study a class of modules which is proper generalization of both the purely extending modules and uniform-extending modules. We call an R-module M is purely uniform-extending if every uniform submodule of M is essential in a pure submodule of M. Many characterizations and properties of purely uniform- extending modules are given. Also, we discuss when a direct sum of purely uniform- extending modules is purely uniform- extending. Key words: Extending modules, purely extending modules, uniform extending modules, purely uniform extending | ||
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