Geodesic
RADICAL FORMULA AND WEAKLY PRIME SUBMODULES
Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 405-412

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DOI

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.
DOI : 10.1017/S0017089509005072
Mots-clés : 13C99, 13C13, 13E05, 13F05, 13F15 
AZIZI, A. RADICAL FORMULA AND WEAKLY PRIME SUBMODULES. Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 405-412. doi: 10.1017/S0017089509005072
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