Geodesic
φ-PRIME SUBMODULES
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 253-259

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let (M) be the set of all submodules of M, and φ: (M) → (M) ∪ {∅} be a function. We say that a proper submodule P of M is a prime submodule relative to φ or φ-prime submodule if a ∈ R and x ∈ M, with ax ∈ P ∖ φ(P) implies that a ∈(P :RM) or x ∈ P. So if we take φ(N) = ∅ for each N ∈ (M), then a φ-prime submodule is exactly a prime submodule. Also if we consider φ(N) = {0} for each submodule N of M, then in this case a φ-prime submodule will be called a weak prime submodule. Some of the properties of this concept will be investigated. Some characterisations of φ-prime submodules will be given, and we show that under some assumptions prime submodules and φ1-prime submodules coincide.
DOI : 10.1017/S0017089509990310
Mots-clés : 13C05 
ZAMANI, NASER. φ-PRIME SUBMODULES. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 253-259. doi: 10.1017/S0017089509990310
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