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Modules With Chain Conditions On δ -Small Submodules | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 55, Issue 1, 2014, Pages 218-223 | ||
| Authors | ||
| Wasan Khalid Hasan; Sahira Mahmood Yaseen | ||
| Abstract | ||
| Let R be an associative ring with identity and M be unital non zero R-module. A submodule N of a module M is called a δ-small submodule of M (briefly N << M )if N+X=M for any proper submodule X of M with M/X singular, we have X=M . In this work,we study the modules which satisfies the ascending chain condition (a. c. c.) and descending chain condition (d. c. c.) on this kind of submodules .Then we generalize this conditions into the rings , in the last section we get same results on δ- supplement submodules and we discuss some of these results on this types of submodules. | ||
| Keywords | ||
| small submodule; supplement submodules; singuler submodule | ||
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