@article {
author = {Ghashghaei, E. and Namdari, M.},
title = {On strongly dense submodulesâ€Ž},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {42},
number = {3},
pages = {731-747},
year = {2016},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $N\leq_{sd}M$, if for any index set $I$, $\prod _{I}N\leq_{d}\prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'\subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'\bigcap N=0$. We also introduce a class of modules in which the two concepts of strong essentiality and strong density coincide. It is also shown that for any module $M$, dense submodules in $M$ are strongly dense if and only if $M\leq_{sd} \tilde{E}(M)$, where $\tilde{E}(M)$ is the rational hull of $M$. It is proved that $R$ has no strongly dense left ideal if and only if no nonzero-element of every cyclic $R$-module $M$ has a strongly dense annihilator in $R$. Finally, some appropriate properties and new concepts related to strong density are defined and studied.},
keywords = {Strongly essential submodule,strongly dense submodule,singular submodule,special submodule,column submodule},
url = {http://bims.iranjournals.ir/article_809.html},
eprint = {http://bims.iranjournals.ir/article_809_9508d8b8a48f740c5b8f741a57040ea9.pdf}
}