… prime if and only if either M is torsion-free or M non-singular. More results on prime and primary
submodule … is 𝑆(𝑁) −locally prime submodule, then 𝑁𝑃 is a prime submodule in 𝑀𝑃 and …

… prime submodules called β-prime submodules. However, we will not mention about studying
properties of β-prime submodules. … of φ-β-prime submodules. Now, we define the notations …

… ΓR-submodule of ΓR-module which represent generalization N-prime submodules. … In
this section we illustrate the concept of nearly prime ΓR-submodule and introduce some basic …

… a new concept of φ-prime submodule over an associative ring … Then we examine the properties
of φ-prime submodules and … submodule, on the other hand it may not be φ∅−prime. 2. If …

… submodule if whenever a1 ··· an+1m ∈ N for some non-units … -prime submodules as a
generalization of prime submodules… R, then every n-prime submodule of M has the form m1 ··· mtM …

… Let R be a commutative ring with unity and K be a submodule of a non-zero left R-module
D… of the prime submodule, which is called R-prime. We prove some properties of the R-prime …

… A proper submodule P of M is called a prime submodule if … If P is a prime submodule of
M, then p = (P :R M) is a prime … ϕ-second submodules where ϕ is a function on the set of all …

… prime submodules, radN is M (see, for example, [11,14,17]). A submodule N of M is called a
radical submodule if … is a unary operation ′ on L and two constants 0 and 1 such that x ∧ x …

… A proper submodule P of M is called a prime submodule if am ∈ P, for a ∈ … Also, a proper
submodule P of M is called a classical prime submodule if … The set of prime(resp. classical …

… If N is an irreducible and weakly semiprime submodule of M, then we prove that (N :R M)
is a prime ideal of R. As a result, we obtain that if p is an irreducible ideal of a ring R such that …