… of two submodules of a multiplication module and … prime submodules of multiplication
submodules. Finally, we state and prove a version of Nakayama lemma for multiplication modules…

… prime submodule of M. By a mtntmar prtme submoduLe N of M we mean a prime submodule
which is minimal in the collection of prime submodules of M. If A is a proper ideal of R then …

… For a ring A, a right A-module M is called a multiplication module if for every submodule N of
M, … If N is a proper submodule of the multiplication module M, then we obtain a contradiction …

… multiplication module M over a ring R such that M does not embed in R. No example of a
faithful multiplication module M R … 4 an example of faithful multiplication module N over a Von …

… An R-module M is called a multiplication module if for each submodule N of M, N = IM for …
(2) If M is finitely generated, then M is a multiplication module if and only if Spec(M) is a spectral …

… For any submodule N of an R-module M, we define V(N) to be the set of all prime submodules
of M containing N. We define the M-radical of a submodule N of an R-module M (denoted …

… A submodule Κα M of a right -module M is prime if for any meM and r 6 Jf? such that mR11£
… a given prime submodule K<M various ways of building new related prime submodules are …

… We also prove that NN (0) is a prime submodule of M if and only if XN is irreducible (…
submodule N as N = IM , where I is an ideal of R, and the module M as a multiplication module …

… module of length 3, its proper submodules are isomorphic to JR/jqJR, R/x2R … modules is
uniserial and hence a multiplication module, we get M is a generalized multiplication module. It …

… All rings are assumed to be associative and with nonzero identity element; all modules are
… ., left) A-module M is said to be a multiplication module if for each of its submodules N, there …