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|Title:||On commutative Noetherian rings which have the s.p.a.r. property|
|Source:||Man, S.H. (1998). On commutative Noetherian rings which have the s.p.a.r. property. Archiv der Mathematik 70 (1) : 31-40. ScholarBank@NUS Repository.|
|Abstract:||Let R be a commutative ring with 1 and M be an unitary R-module. Prime and semiprime submodules of M are defined as follows. An R-submodule P of M is called a prime submodule of M if (i) P ≠ M, and (ii) whenever rm ∈ P for some r ∈ R, m ∈ M\P, then rM ⊆ P. An R-submodule N of M is called a semiprime submodule of M if (i) N ≠ M, and (ii) whenever rk m ∈ N for some r ∈ R, m ∈ M and natural number k, then rm ∈ N. It is clear that an intersection of prime submodules of M is a semiprime submodule of M. In this paper, we give a characterization of a commutative Noetherian ring R with property that, every semiprime submodule of an R-module is an intersection of prime submodules.|
|Source Title:||Archiv der Mathematik|
|Appears in Collections:||Staff Publications|
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