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Modules Whose Nonzero Finitely Generated Submodules Are Dense
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نویسنده
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Hajikarimi A.
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منبع
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Journal Of Algebraic Structures And Their Applications - 2021 - دوره : 8 - شماره : 1 - صفحه:89 -97
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چکیده
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Let r be a commutative ring with identity and m be a unitary r-module. first, we study multiplication r-modules m where r is a one dimensional noetherian ring or m is a finitely generated r-module. in fact, it is proved that if m is a multiplication r-module over a one dimensional noetherian ring r, then m ∼= i for some invertible ideal i of r or m is cyclic. also, a multiplication r-module m is finitely generated if and only if m contains a finitely generated submodule n such that annr(n) = annr(m). a submodule n of m is called dense in m, if m = σ φ φ(n) where φ runs over all the r-homomorphisms from n into m and r-module m is called a weak π-module if every non-zero finitely generated submodule is dense in m. it is shown that a faithful multiplication module over an integral domain r is a weak π-module if and only if it is a prüfer prime module.
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کلیدواژه
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Dense Submodules ,Multiplication Modules ,Prime Modules ,Weak Π-Modules
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آدرس
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Islamic Azad University, Mobarakeh Branch, Department Of Mathematics, Iran
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پست الکترونیکی
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a.hajikarimi@mau.ac.ir
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Authors
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