… A proper submodule N of M is called a classical prime submodule, if for each m ∈ M …
classical prime submodules”. A proper submodule N of M is a weakly classical prime submodule if …

… of φ-classical prime submodules. We define an (n − 1,n)-φ-classical prime submodule of
M and investigate a number of results concerning (n − 1,n)-φ-classical prime submodules…

… Suppose a classical prime submodule P is IFP, we show that P is classical completely prime.
If a, b ∈ R and m ∈ M such that abm ∈ P, then aRbm ⊆ P and aRb(Rm) ⊆ P so that aRb〈…

… Starting from a given prime submodule K<M various ways of building new related prime
submodules are developed. The previous notation is continued in particular for …

… of graded classical prime submodule of … is a classical prime submodule of the Re-module
Mg for every g∈ G. It is evident that every graded prime submodule is graded classical prime. …

… studied the same notion under the name ”classical prime submodule”, and in this paper we
prefer to use classical prime submodule instead of weakly prime submodule. The notion of …

… of prime ideals of R to prime submodules, see [10], [5], [8], [9], [12]. For example, the classical
result of Cohen’s is extended to prime submodules … only if every prime submodule is finitely …

… some classical modules … all prime submodules and all S-prime submodules by Spec(RM)
and SpecS(RM), respectively. In particular, we write SpecS(R) to express the set of all S-prime …

… submodule P of M is called a classical prime submodule if … A proper submodule P of M is
called a prime submodule if … a proper submodule P of M is called a classical prime submodule if …

0. Introduction. Let R be a ring. A proper left ideal L of R is prime if, for any elements a and b
in R such that aRb CL, either a€ L or b 6 L. For example, any prime two-sided ideal is a …