… -module with unitary. In this paper, we introduce a new concept of φ-prime submodule over
an associative ring … a multiplication R-module and R be a von-Neumann regular ring. Let I ⊆ …

… ℘-serial modules over commutative rings. Also, we study ℘-serial modules over almost perfect
… Assume that N is a prime submodule of M, a is a regular element of R and x ∈ N. Then …

… regular module in the sense [13]. Let 𝐴 be a commutative ring with 1 ≠ 0 and 𝑋 a multiplication
𝐴-module. 𝑋 is … We show that 𝑞-prime submodule 𝑌 of a fg multiplication module 𝑋 is a …

… If there is no prime submodule containing N, we define radM (N) = M. A submodule N of M
is … generated von Neumann regular modules in terms of d-submodules (see Theorem 2.25). …

… simple) R-module if and only if R is a von Neumann regular ring. More … modules over
commutative rings. Recall that an R-module M is a multiplication module if for each R-submodule N …

… regular module over a commutative ring to a V N-regular module over a ring which is not
necessarily commutative… MV Nregular if aM = a2M where R is a commutative ring and M is an R-…

… We show that regular divisors extend the concept of divisors to submodules of finitely
generated modules over Noetherian rings. If n is an integer, then d is a divisor of n if and only if dZ …

… counting the number of Q-prime submodules of F when Q is a … We refer the reader to standard
texts of graph theory such as [… is said to be regular of degree r or r-regular. A hypergraph is …

… If M is a multiplication module over von Neumann regular ring R and N ≤ … prime submodules
under a certain condition by using the S-closed subsets in modules over commutative rings…

… It is shown that, a finitely generated module M is completely ℘ -virtually semisimple module
if … module over a commutative ring is semisimple, then R is a von Neumann regular ring (see …