… chains of prime submodules and we shall improve the results given in [9]. The prime avoidance
… On the other hand, since by assumption we have (N0 :R M) = p, it follows that there is an …

… In this research note approximately prime submodules is defined as a new generalization
of prime submodules of … A proper submodule of an -module is called an approximaitly prime …

… Furthermore, the set of all zero divisors on M is denoted by z(… prime submodules and
torsion-free modules. Let S be a mcs of R. A submodule P of M is said to be an S-prime submodule …

… on the set Spec(M) of all prime submodule elements of M. Thus, we extend many results on
… of quasi-compact open sets for the Zariski topology on Spec(M). Every irreducible closed …

… the properties of uniformly primal submodules. Also, we generalize the prime avoidance
theorem for … Then, we will prove some results on the S-system and uniformly primal submodule. …

… Abstract: The subject of this paper is the Zariski topology on a multiplication module M
over … We also prove that NN (0) is a prime submodule of M if and only if XN is irreducible (Theorem …

… 2-prime submodules as a generalized concept of 2prime ideal, where proper submodule H
of module F over a ring R is said to be 2prime if … R satisfies dcc on 2-prime, it follows that such …

… We call an R-submodule of as P-essential if for each nonzero prime submodule of and 0 …
Proof : Let P be a prime submodule of ́ and let be a non-zero submodule of . Since is an …

… Aproper RΓ-submodule E of G is said to be S-prime (S-semiprime) RΓ-submodule of G
whenever … RΓ-submodule E of G is said to be S-prime RΓ-submodule whenever E K ⊆ ) …

… Occasionally as well as occasionally based on what’s needed, it has been … Prime submodules
and characterize some of the attributes of has been classification of submodules…