Finitely Coatomic Modules

Abstract

In this paper, we introduce finitely coatomic modules. We prove that any direct sum of finitely coatomic modules is finitely coatomic. Also we prove, if M is a module with finitely generated Jacobson radical, then M is f-semilocal if and only if M is finitely weakly supplemented and f-coatomic.

Keywords

• Coatomic modules,Supplemented modules,2000 AMS Classification: Primary: 16 D 10

References

1. Alizade, R. and B¨uy¨uka¸sık, E. Cofinitely weak supplemented modules, Comm. Algebra 31(11), 5377–5390, 2003.
2. G¨ung¨oro˘glu, G. Coatomic Modules, Far East J. Math. Sciences, Special volume 2, 153–162, 1998.
3. G¨ung¨oro˘glu, G. and Harmancı, A. Coatomic Modules over Dedekind Domains, Hacettepe Bulletin of Natural Sciences and Engineering Series B 28, 25–29, 1999.
4. Lomp, C. On semilocal modules and rings, Comm. Algebra 27 (4), 1921–1935, 1999.
5. Rudlof, P. On the structure of couniform and complemented modules, J. Pure Appl. Algebra 74(3), 281–305, 1991.
6. Z¨oschinger, H. Koatomare Moduln, Math. Z. 170, 221–232, 1980.
7. Z¨oschinger, H. Komplemente als direkte Summanden III, Arch. Math. (Basel) 46 (2), 125– 135, 1986.