… If P is a prime submodule, then p = (P :R M) is necessarily a prime … prime submodules and
saturations of submodules. In this short paper, some properties of saturations of submodules …

… A submodule 𝑁of an 𝑅-module 𝑀is called prime, if 𝑟𝑚 ∈ 𝑁, … 𝑅 𝑀) is a prime ideal of 𝑅 and
𝑁is called 𝑝 −prime. Consider 𝜌:… module, we consider 𝐿 as a submodule of 𝑀 and 𝑁 = 𝑀/𝐿, so …

… A sub-module N of M is called a prime sub-module if every time 𝑟 ∈ 𝑅,𝑚 ∈ 𝑀, 𝑟𝑚 ∈ 𝑁, …
a weakly prime sub-module of M. Every prime submodule is also a weak prime sub-module, …

… In this paper, we present the dual notion of jointly prime (R, S)-submodules, that is … )-submodule
P of M is called jointly prime if for any ideal I of R, ideal J of S, and (R, S)-submodule N of …

… For a prime number p, one can see that the submodule pZ of the Z-module Z is not pure. …
By focusing on first coordinate, we have s1(N1 ∩I1M1) ⊆ I1N1. Hence, M1 is a fully S1-pure R1…

… M on a ring R (not necessarily commutative) is called prime if for every nonzero submodule
K … We recall that an R-module M is called a multiplication module, if every submodule N of M …

… Semi-prime submodules (modules). Our aim is to study dــSmall Semi-prime submodules (…
Many researches are present on the generalizations of these notions; see [2, 3]. Consider 𝐴 …

… The reader is referred to [9] and [16] for results on the category σ[M]. It is an abelian category,
… In Section 5, we show that the notion of a prime (semiprime) submodule is Morita invariant, …

… of graded prime submodules and we investigate some properties of such graded submodules.
… Tekir and AG Agargün, On graded prime and primary submodules, Turkish J. Math., 35 (…

… absorbing Ie-prime submodule as a new generalization of a graded 2-absorbing prime
submodule on the one hand and a generalization of a graded Ie-prime submodule on other hand…