# 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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- [6] S.H. Mohamed and B.J. Müller: Continuous and discrete modules, London Math. Soc. LNS 147, Cambridge Univ. Press, Cambridge, 1990.
- [7] R. Wisbauer: Foundations of Module and Ring Theory, Gordon and Breach, Reading, 1991.
- [8] Y. Zhou: “Generalizations of Perfect, Semiperfect and Semiregular Rings”, Algebra Colloquium, Vol. 7(3), (2000), pp. 305–318. http://dx.doi.org/10.1007/s10011-000-0305-9 Zbl0994.16016
- [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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