Essential submodules relative to a submodule
Publish place: The Journal of Algebra and Related Topics، Vol: 11، Issue: 2
Publish Year: 1402
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JART-11-2_004
تاریخ نمایه سازی: 21 تیر 1403
Abstract:
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.
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Authors
S. Rajaee
Department of Mathematics, University of Payame Noor,Tehran, Iran.