… of all prime submodules of M containing N. Recall that a proper submodule N of M is said to
be prime if am ∈ N … We say that M is a prime module if the zero submodule of M is a prime …

… -submodule of RΓ-module besides some of its basic properties. In this paper, Z-prime RΓ-submodule …
In addition, the relation between Z- prime RΓ-submodule with other RΓ-modules is …

… in any prime, then the radical of A is defined to be radL (A) = L. Further, L ̸= A is said to be
radical (in L) if A = radL(A). Prime B of a submodule A of L can be lifted to L if there is prime C …

… a prime ideal of R and we call K a P-prime submodule of M. This notion of prime submodule
was … On the other hand, since M is a torsion-free divisible R-module, then, for each nonzero …

… that we will rely obtain some important results on the topic (semi-… But in this research we will
rely on the semi-essential … if for every non-zero prime subsemimodule ℬ of 𝒲 then 𝒱 ∩ ℬ ≠ …

… as results on finitely generated multiplication modules. Also, we prove that for every submodule
N of … of all prime submodules P of M such that (P :R M) ∩ S = ∅ onto Spec(MS). Now, use …

… There has been a great deal of studding on prime submodules and their generalizations.
For more knowledge about … We focus on the torsion elements of M and we denote Tor M …

… submodules is quite different from the class of strongly prime submodules and the class of
primary submodules. … Pusat-Yılmaz, On prime submodules of finitely generated free modules, …

… of graded Jgr-classical prime submodule as a new generalization of graded classical submodule
and we give some results … We say that a proper graded submodule N of M is a graded …

… -prime ideal if I is an S-prime submodule of R-module R. We denote the sets of all prime
submodules and all S-prime submodules … -prime submodules and prime submodules are equal. …