… if ϕ(N)=(N : M)n-1N, then we say that N is n-almost prime submodule. … -1P is a weakly prime
submodule of S … want to generalize this fact for (n − 1,n) − ϕ-prime submodules. Let N(S) = …

… As a generalization of the concept of prime submodules, a proper submodule N of M will be
called n-almost prime, if for r ∈ R and x … We study n-almost prime submodules, in this paper. …

… of prime submodules. It lists seven conditions each of which is equivalent to that a proper
submodule of a module is prime. … module, we consider a generalization of this fact of projective …

… generalization of φ-classical prime submodules. We define an (n − 1,n)-φ-classical prime
submodule … concerning (n − 1,n)-φ-classical prime submodules. Let M be an R-module and φ : …

… -prime submodule and prove analogous of some of the properties of φ-prime ideals of
commutative ring for φ-prime submodules. … the results of prime ideals of commutative ring to prime …

… , and any weakly primary submodule is almost primary submodule. However … prime submodule
which is not weakly prime, we consider the Z-module M = Z24 and the proper submodule …

… A submodule Κα M of a right -module M is prime if for any meM and r 6 Jf? such that mR11£
… and monoform modules generalize to the module setting. Some of these generalizations are …

… submodule K of M and elements a, b ∈ R, abK ⊆ N implies that aK ⊆ N or bK ⊆ N. Weakly
prime submodules are generalizations of prime submodules … a weakly prime submodule of M…

… a prime submodule P of any module A and a free preimage F of A, the preimage of P is prime
in F… 1 The remaining two results of this section generalize Lemma 2.7 and Lemma 2.8 of [hl, …

… In this note we give two generalizations of Anderson’s result. First we show that … generalization
of Cohen’s Theorem. We also extend Anderson’s Theorem to minimal prime submodules …