SOME RESULTS ON STRONGLY PRIMESUBMODULES
Publish place: Journal of Algebraic Systems، Vol: 1، Issue: 2
Publish Year: 1393
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JAS-1-2_001
تاریخ نمایه سازی: 13 مرداد 1394
Abstract:
Let R be a commutative ring with identity and let M be an R-module. A proper submodule P of M is called stronglyprime submodule if (P +Rx : M)y ? P for x; y € M, implies that x € P or y € P. It is shown that a nitely generated R-module Mis Artinian if and only if M is Noetherian and every strongly prime submodule of M is maximal. We also study the strongly dimensionof a module which is de ned to be the length of a longest chain of strongly prime submodules.
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