… In this article, we study rings and modules in which every prime submodule is isomorphic
to … for rings or modules “on the left,” then we shall also use such results freely “on the right,” …

… A graded R-submodule N of M is said to be graded gw-prime … prime submodules are first
introduced by SE Atani in [10]. A graded R-submodule N of M is said to be graded weakly prime …

… Based on [7], we have that an R-module M is called a fully weakly prime module if each
proper submodule of M is weakly prime. When we extend these facts to (R, S)-module, we have …

… on the prime spectra of modules over rings; for example, see [1], [3], [20], [21], [22], [28], [30],
[31], [32]. The set of all prime … But, it is not the case for the set of all prime submodules of a …

… We note that the zero submodule in any module is always weakly prime regarding the sense
used in [9, 12]. However… We give a similar result for a weakly prime submodule of a module. …

… We prove many properties for this kind of submodules. Every 2-prime submodule is quasi-prime
submodule but the converse is not true, and K be a submodule of an R-module W. Then, …

… submodules of M such that Mi−1 is aqi-prime submodule of Mi, then we say the generalized
prime … We define a relation ∼ on S as (p1,..., pr) ∼ (q1,..., qs), if (q1,..., qs) is a permutation of …

… Every prime submodule is a generalized prime submodule but the opposite is not true in …
𝒵12 is not a prime submodule of 𝒵12, but it is a generalized prime submodule of 𝒵12 [18]. …

… In this paper ,WAPP-quasi prime submodules are introduced as new … quasi prime submodules
, where proper submodule C of an R-module T is called WAPP –quasi prime submodule …

… submodule µ of M is said to be prime fuzzy (or fuzzy prime) if for ζ ∈ FI(R) and ν ∈ FS(M)
such that ζ.ν ⊆ µ, then either ν ⊆ µ or ζ ⊆ (µ : 1M ). If M = R, then µ is said to be a fuzzy prime …