… prime submodules have been introduced by Atani in [12]. A proper graded R-submodule N
of M is said to be graded prime if … Graded prime submodules have been widely studied by …

… submodule of a module to be an n-submodule. Also, we show that if M is a finitely generated
R-module and √AnnR(M) is a prime ideal of R, then M has n-submodule. … prime submodule …

… In the next lemma we observe that every prime submodule in … N be a prime submodule of
M. Then N is strongly irreducible … On the other hand, in view of Proposition 2.6 the submodule …

… It is clear that a prime submodule is a 1-absorbing primary submodule, and a 1-absorbing
primary submodule is a 2-absorbing primary submodule. In Section 2, we start with examples (…

… the notion of prime ideal factorization to submodules of a finitely … We say a submodule K of
M is a p-prime extension of a … each prime ideal do not depend on any particular RPE filtration. …

… as weakly primary , weakly quasi primary and weakly semi prime submodules see [7 ,8 ,9] .
… weakly prime submodule called WAPP-prime submodule . Recall that a nonzero submodule …

… Since N is a prime submodule and a /∈ (N :R M), we get x ∈ N and so N is an n-… On the
other hand, pM is the only prime submodule of M. So N = pM and (N :R M)=(pM :R M) = pZ, …

… submodules called WE-primary submodules and the other of a subclass of weakly quasi-prime
submodules called WE-quasi-prime submodules. … On the otherhand, the homeorphic and …

… proper submodule of is called a quasi-prime submodule… prime submodules, in this paper
we introduce the concept of approximaitly quasi-prime submodules, where a proper submodule …

… Prime submodules have been an important … prime submodules see [1, 2, and 3]. In this note
we introduced new generalization of prime submodule named Alappn prime submodule and …