On prime submodules and primary decomposition
We characterize prime submodules of for a principal ideal domain and investigate the primary decomposition of any submodule into primary submodules of
On some classes of modules
The aim of this paper is to investigate quasi-corational, comonoform, copolyform and -(co)atomic modules. It is proved that for an ordinal a right -module is -atomic if and only if it is -coatomic. And it is also shown that an -atomic module is quasi-projective if and only if is quasi-corationally complete. Some other results are developed.
Central Armendariz rings.
Generalizations of coatomic modules
For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N+X=M with M/X singular, we have X=M. Let ℘ be the class of all singular simple modules. Then δ(M)=Σ{ L≤ M| L is a δ-small submodule of M} = Re jm(℘)=∩{ N⊂ M: M/N∈℘. We call M δ-coatomic module whenever N≤ M and M/N=δ(M/N) then M/N=0. And R is called right (left) δ-coatomic ring if the right (left) R-module R R(RR) is δ-coatomic. In this note, we study δ-coatomic modules and ring. We prove M=⊕i=1n Mi...
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