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Generalizations of coatomic modules

M. Koşan;  Abdullah Harmanci — 2005

Open Mathematics

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...

On some classes of modules

Gonca Güngöroglu;  Harmanci, Abdullah — 2000

Czechoslovak Mathematical Journal

The aim of this paper is to investigate quasi-corational, comonoform, copolyform and α -(co)atomic modules. It is proved that for an ordinal α a right R -module M is α -atomic if and only if it is α -coatomic. And it is also shown that an α -atomic module M is quasi-projective if and only if M is quasi-corationally complete. Some other results are developed.

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