Generalizations of coatomic modules |
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Authors: | M Tamer Koşan Abdullah Harmanci |
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Institution: | (1) Department of Mathematics, Faculty of Sciences and Arts, Kocatepe University, Afyon, Turkey;(2) Department of Mathematics, Faculty of Science, Hacettepe University, 06532 Beytepe, Ankara, Turkey |
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Abstract: | 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=1
n
Mi is δ-coatomic if and only if each M
i (i=1,…, n) is δ-coatomic. |
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Keywords: | δ -small module coatomic module |
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