Research Paper | Mathematics | Iraq | Volume 7 Issue 1, January 2018
R-Annihilator - Hollow Modules
Hala K. Al-Hurmuzy
Let R be an associative ring with identity and let M be a unitary left R- module.We call a non-zero module M, R-annihilator hollow module if every proper submodule of M is R-annihilatorsmall submodule of M..The sum A_M of all such submodules of M contains the Jacobson radical J (M) and the singular submodule Z (M).When M is finitly generated and faithful, we study A_M and K_M in this paper.Conditions when A_M is R-annihilator-small and K_M= A_ (M ), J (M) A_Mand Z (M) A_M are given.
Keywords: hollow modules, annihilators, R-annihilator- hollow modules
Edition: Volume 7 Issue 1, January 2018
Pages: 400 - 402
How to Cite this Article?
Hala K. Al-Hurmuzy, "R-Annihilator - Hollow Modules", International Journal of Science and Research (IJSR), https://www.ijsr.net/search_index_results_paperid.php?id=ART20178614, Volume 7 Issue 1, January 2018, 400 - 402
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