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• # Artykuł - szczegóły

## Open Mathematics

2005 | 3 | 2 | 273-281

## Generalizations of coatomic modules

EN

### Abstrakty

EN
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.

EN

273-281

wydano
2005-06-01
online
2005-06-01

### Twórcy

autor
• Kocatepe University
autor
• Hacettepe University

### Bibliografia

• [1] F.W. Anderson and K.R. Fuller: Rings and Categories of Modules, Springer-Verlag, New York, 1974.
• [2] K.R. Goodearl: Ring Theory: Nonsingular Rings and Modules, Dekker, New York, 1976.
• [3] G. Gungoroglu: “Coatomic Modules”, Far East J. Math. Sci., Special Volume, Part II, (1998), pp. 153–162.
• [4] F. Kasch: Modules and Rings, Academic Press, 1982.
• [5] C. Lomp: “On Semilocal Modules and Rings”, Comm. Alg., 27(4), (1999), pp. 1921–1935.
• [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
• [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.