… prime submodules of M containing N. We define a proper submodule N of M to be a weakly
semiprimary submodule … \), then we conclude that L is not a weakly prime submodule of \(M'\). …

… Every prime submodule is rad-semiprime submodule. The converse is not true in general
for example: A submodule 6Z of Z as Z-module is rad-semiprime submodule, but not prime …

… classical S-primary submodule and graded classical S-prime submodule. In Section Two, …
classical S-primary submodule. We say that P is a graded classical S-primary submodule of R-…

… prime submodules of M containing N is called the radical of N and denoted by radN. If there
is no prime submodule … a primary-like submodule of M that is not a prime submodule of M. It …

… it is determined uniquely by M and it does not depend on the choice of the set of generators
of M [… Assume that \({{\,\mathrm{T}\,}}(M)\), the torsion submodule of M, be the submodule of M …

… lattice L on M similar to the action of a ring on a module. A lattice module M abstracts the
complete lattice Sub(A) of … Now we introduce prime submodule elements of an le-module RM. …

… ) submodule of a module Φ(M). We show that a nonnil prime submodule N of an R-module
M is a Φ-powerful submodule if and only if it is a Φ-strongly prime submodule. Similarly, if …

… In this paper, we study the property of being prime or essential for annihilator submodules
of M. Also, we introduce the annihilator essential graph of equivalence classes of zero divisors …

… on small submodules were described in [1]. A submodule N is called a prime submodule if
… On the other hand, we may classify some submodules of M generating the factor modules …

… [3], where a proper submodule 𝐵 of an R-module D is called prime submodule, if … submodule
as a generalization of prime submodule was introduced by [2], where a proper submodule …