… and modules. In Sec. 4 we give several equivalent conditions for a module to be fully (almost
fully) weakly prime module. … Similarly, we call an R-module M a fully weakly prime module if …

… as an R-module, then prime submodules and weakly prime … relations between weakly prime
submodules of M and weakly prime … between weakly prime submodules N of M with ZdR(M …

… weakly prime radicals of modules and show that for Ore domains, the study of weakly prime
radicals of general modules … the notions of prime module and weakly prime module, we have …

… of M is called weakly prime if for r … prime submodule of a module is a weakly prime submodule.
However, since 0M is always weakly prime, a weakly prime submodule need not be prime…

… in any module is always weakly prime. However, in Z30 as Z-module, (0) is not weakly prime
… On the other hand, it is easy to see that in Z ⊕ Z as Z-module, (0) ⊕ 2Z is weakly prime …

… For example, we show that if P is a submodule of a finitely generated multiplication R-module
M, then P is weakly prime if and only if for submodules N and K of M with 0 = NK ⊆ P, …

… of the amalgamation module along an ideal … of weakly prime submodules as a generalization
of prime submodules. Following [7], a proper submodule N of M is said to be weakly prime …

… ring R is weakly prime if whenever a, b ∈ R with 0 = ab ∈ I, then a ∈ I or b ∈ I. Weakly prime
submodules … First of all we give a module which has no nonzero weakly classical prime sub…

… In the following, we show that the notion of weakly prime … any module is always weakly
prime regarding the sense used in [9, 12]. However, in Z30 as a Z-module, (0) is not weakly prime …

… Let R be a commutative ring containing a unit, and let M be a left R-module. We define a
proper sub-module N of an R-module M to be a weakly 2-prime sub-module if whenever 0 ≠ …