… R-module M is a prime module if and only if every nonzero cyclic submodule of M is a dense
submodule of … that, for modules with nonzero socles and for co-semisimple modules, the two …

… a prime jR-module is faithful and every submodule of a prime i^-module is a prime i^-module…
Since S is a dense ring of linear transformations acting on Q ®A M, we have xab~l = y for …

… faithful multiplication module over an integral domain, then a submodule N of M is dense in
… is easily seen that the Z-module Z CB Q is a prime module but not a x module. (See Ex. 1.4.) …

… monoform modules. In Section 4, we introduce and study submodules corresponding to the
concept of dense … M is strongly monoform if and only if M is a strongly uniform prime module. …

… R-module M is said to be monoform if any nonzero submodule of M is a dense submodule,
… We recall that a nonzero R-module M is said to be a prime module if AnnR(N) = AnnR(M) for …

… We will refer to it as a free dense submodule of M. … As a first application of the existence of
a free dense submodule … P is a submodule of M, we consider P as a right R-module. So Z(P) …

… of pseudo-prime submodule of modules resembles to that theory of prime ideals of rings. …
(2) If (0) ∈ Y , then Y is dense in XM ; (3) XM is a T0-space; (4) XM is a T1-space if and only …

… D ⊆ X is said to be dense in X if for every nonempty open … Zariski topology of a submodule
N in a module M . We show that … We also prove that NN (0) is a prime submodule of M if and …

… ring of a torsionless module over a dense ring of … concerning essential submodules, singular
submodules, and other … We remark that prime modules in this sense are prime in the sense …

… module over noncommutative discrete valuation rings has a basic submodule and that any
basic submodules of the module … that θ maps continuosly onto a dense submodule of Π MP …