Generalizations of coatomic modules
M. Koşan ; Abdullah Harmanci
Open Mathematics, Tome 3 (2005), p. 273-281 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:268730 
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     author = {M. Ko\c san and Abdullah Harmanci},
     title = {Generalizations of coatomic modules},
     journal = {Open Mathematics},
     volume = {3},
     year = {2005},
     pages = {273-281},
     zbl = {1106.16005},
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M. Koşan; Abdullah Harmanci. Generalizations of coatomic modules. Open Mathematics, Tome 3 (2005) pp. 273-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02479203/

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