… a proper submodule N of an R-module M a prime submodule of M if M/N is a prime module,
… , it must be semisimple, for each of its nonzero cyclic submodules is a regular module with …

… A ring R is prime if and only if the right annihilator of every non-zero right ideal is … modules
having the properties that the annihilator in R of every non-zero submodule is zero and regular …

… submodule N of M, ie, rx = 0 for x ∈ M, r ∈ R implies that x = 0 or rM = (0). We call a proper
submodule N of an R-module M a prime submodule … -module if and only if R is a regular ring (…

… (N : M)n-1N, then we say that N is n-almost prime submodule. … multiplication modules in
which every proper submodule is a … regular, for all i ∈ {1,2,...,m}, hence M is regular. If M1 is not …

… submodule of M is a direct summand of M. Every countably (or finitely) generated submodule
of M is a direct sum of cyclic regular modules… a cyclic submodule Rm of a regular module M …

0. Introduction. Let R be a ring. A proper left ideal L of R is prime if, for any elements a and b
in R such that aRb CL, either a€ L or b 6 L. For example, any prime two-sided ideal is a …

… new equivalent conditions for a minimal prime submodules of an R-module to be a finite set,
… finitely generated R-module. For each p-prime submodule N of M we define height of N as: …

… R-submodule is an intersection of maximal Rsubmodules. … over a commutative ring R is
regular, then every simple … We shall prove this result for general regular modules over commuta…

… A is (von Neumann) regular iff every left (or right) … regular modules as modules all of whose
submodules are pure. The ring A is then regular iff all its left (or right) ^-modules are regular. …

… notion of prime submodule and call it weakly prime submodule. A proper submodule P of
M is called a … We call an R-module M compatible if its prime submodules and its weakly …