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Generalizations of coatomic modules

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Koşan M., Harmanci A.

Open Mathematics

2005

tom 3

nr 2

273-281

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 is δ-coatomic if and only if each M i (i=1,…, n) is δ-coatomic.

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1 Open Mathematics

1 Harmanci A.

1 Koşan M.

1 2005

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Generalizations of coatomic modules