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Essential submodules relative to a submodule | ||
Journal of Algebra and Related Topics | ||
دوره 11، شماره 2، اسفند 2023، صفحه 59-71 اصل مقاله (312.46 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22124/jart.2023.23331.1465 | ||
نویسنده | ||
S. Rajaee* | ||
Department of Mathematics, University of Payame Noor,Tehran, Iran. | ||
چکیده | ||
In this paper, our aim is to introduce and study the essential submodules of an $R$-module $M$ relative to an arbitrary submodule $T$ of $M$. Let $T$ be an arbitrary submodule of an $R$-module $M$, then we say that a submodule $N$ of $M$ is an essential submodule of $M$ relative to $T$, whenever for every submodule $X$ of $M$, $N\cap X\subseteq T$ implies that $(T:M)\subseteq ^{e}{\rm Ann}(X)$. We investigate some new results concerning to this class of submodules. Among various results we prove that for a faithful multiplication $R$-module $M$, if the submodule $N$ of $M$ is an essential submodule of $M$ relative to $T$, then $(N:M)$ is an essential ideal of $R$ relative to $(T:M)$. The converse is true if $M$ is moreover a finitely generated module. | ||
کلیدواژهها | ||
Multiplication module؛ faithful module, essential submodule | ||
آمار تعداد مشاهده مقاله: 178 تعداد دریافت فایل اصل مقاله: 249 |