… of prime submodule and call it strongly prime submodule. First … We say that P is a strongly
prime submodule if , for x,y ∈ M, … submodule C of M to be a strongly semiprime submodule if , …

… introduced in [11] coincide with the prime submodules. However, the strongly prime
submodules in this paper are special cases of prime submodules (see (1)(2)). …

… In the first section of this paper, we generalize the notion of strongly prime ideal to a
prime submodule of a torsion free R-module and obtain results which characterize it. In the …

… to modules via strongly prime submodules such that all Artinian modules with a maximal (…
strongly prime submodule. Suppose to the contrary that P is not a strongly prime submodule…

… This shows P is a prime submodule and hence a classical prime submodule. We construct
a maximal submodule which is not classical completely prime. Let R = (M2(Z), +, .) be a ring of …

… A submodule Κα M of a right -module M is prime if for any meM and r 6 Jf? such that mR11£
… a given prime submodule K<M various ways of building new related prime submodules are …

… prime submodule as following: A proper submodule N of an R-module M is said to be S-weakly
prime submodule … Clearly, every S-prime submodule is an S-weakly prime submodule. In …

… strongly prime, non-singular prime, and primitive ideals. We prove that if R is a strongly
prime … assumption we prove that every closed prime ideal P of W is strongly prime (resp. non-…

… By setting \(S=\{1\}\), we conclude that every strongly prime submodule is an S-strongly
prime submodule by Proposition 2.2. The following example shows that the converse is not true …

… submodule of My and let Q denote the annihilator of M/K. Then K is called strongly prime if (i)
Q is a prime … Now we consider more general chain conditions on strongly prime submodules…