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Shahram Mehry

Academic rank: Assistant Professor
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Education: PhD.
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Faculty: Mathematical Sciences and Statistics
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Research

Title
On special submodule of modules
Type
JournalPaper
Keywords
Prime submodule, strongly prime submodule, primary submodule, strongly prime submodule, power submodule
Year
2014
Journal Bulletin Of The Iranian Mathematical Society
DOI
Researchers Shahram Mehry

Abstract

Let R be a domain with quotiont eld K, and let N be a submodule of an R-module M. We say that N is powerful (strongly primary) if x; y 2 K and xyM  N, then x 2 R or y 2 R (xM  N or ynM  N for some n  1). We show that a submodule with either of these properties is comparable to every prime submodule of M, also we show that an R-module M admits a powerful submodule if and only if it admits a strongly primary submodule. Finally we study nitely generated torsion free modules over domain each of whose prime submodules are strongly primary