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A Short Note on Prime Submodules
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نویسنده
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A'Zami Jafar
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منبع
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Journal Of Algebraic Structures And Their Applications - 2018 - دوره : 5 - شماره : 1 - صفحه:41 -49
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چکیده
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Let r be a commutative ring with identity and m be a unital r-module. a proper submodule n of m with n :r m = p is said to be prime or p-prime (p a prime ideal of r) if rx ∈ n for r ∈ r and x ∈ m implies that either x ∈ n or r ∈ p. in this paper we study a new equivalent conditions for a minimal prime submodules of an r-module to be a finite set, whenever r is a noetherian ring. also we introduce the concept of arithmetic rankof a submodule of a noetherian module and we give an upper bound for it.
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کلیدواژه
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Arithmetic Rank Of A Submodule ,Associated Primes ,Height Of A Prime Submodule ,Minimal Prime Submodule ,Prime Submodule
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آدرس
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University Of Mohaghegh Ardabili, Faculty Of Sciences, Department Of Mathematics, Iran
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پست الکترونیکی
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jafar.azami@gmail.com
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Authors
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