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RADICAL FORMULA AND WEAKLY PRIME SUBMODULES

Published online by Cambridge University Press:  01 May 2009

A. AZIZI
A. AZIZI*
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran e-mail: aazizi@shirazu.ac.ir
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Abstract

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Let B be a submodule of an R-module M. The intersection of all prime (resp. weakly prime) submodules of M containing B is denoted by rad(B) (resp. wrad(B)). A generalisation of 〈E(B)〉 denoted by UE(B) of M will be introduced. The inclusions 〈E(B)〉 ⊆ UE(B) ⊆ wrad(B) ⊆ rad(B) are motivations for studying the equalities UE(B) = wrad(B) and UE(B) = rad(B) in this paper. It is proved that if R is an arithmetical ring, then UE(B) = wrad(B). In Theorem 2.5, a generalisation of the main result of [11] is given.

Keywords

13C9913C1313E0513F0513F15

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009 , pp. 405 - 412
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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