Generalizations of coatomic modules
Open Mathematics (2005)
- Volume: 3, Issue: 2, page 273-281
- ISSN: 2391-5455
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topM. Koşan, and Abdullah Harmanci. "Generalizations of coatomic modules." Open Mathematics 3.2 (2005): 273-281. <http://eudml.org/doc/268730>.
@article{M2005,
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=1n Mi is δ-coatomic if and only if each M i (i=1,…, n) is δ-coatomic.},
author = {M. Koşan, Abdullah Harmanci},
journal = {Open Mathematics},
keywords = {16D60; 16D99; 16S90},
language = {eng},
number = {2},
pages = {273-281},
title = {Generalizations of coatomic modules},
url = {http://eudml.org/doc/268730},
volume = {3},
year = {2005},
}
TY - JOUR
AU - M. Koşan
AU - Abdullah Harmanci
TI - Generalizations of coatomic modules
JO - Open Mathematics
PY - 2005
VL - 3
IS - 2
SP - 273
EP - 281
AB - 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.
LA - eng
KW - 16D60; 16D99; 16S90
UR - http://eudml.org/doc/268730
ER -
References
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- [9] M.Y. Yousif and Y. Zhou: “Semiregular, Semiperfect and Perfect Rings relative to an ideal”, Rocky Mountain J. Math., Vol. 32(4), (2002), pp. 1651–1671. Zbl1046.16007
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