Strongly Goldie Extending Modules | ||
| Journal of Al-Qadisiyah for Computer Science and Mathematics | ||
| Article 1, Volume 8, Issue 1, June 2016, Pages 54-66 PDF (0 K) | ||
| Authors | ||
| ; ar Younis Ghawi | ||
| Abstract | ||
| A submodule N of a right R-module M is said to be strongly large in case for any m∈M, s∈R with ms≠0, there exists an r∈R such that mr∈N and mrs≠0. In this paper, we introduce strongly G-extending modules which are particular G-extending modules, and investigate their properties and characterizations. An R-module M is called strongly G-extending if for each submodule X of M there exists a direct summand D of M such that X∩D is strongly large in both X and D. Some sufficient conditions for a direct sum of strongly G-extending modules to be strongly G-extending are obtained. Examples to illustrate this concept are given. | ||
| Keywords | ||
| Strongly large submodules; closed submodules; Strongly extending modules; extending modules; Strongly G | ||
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