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Modules that have a supplement in every cofinite extension
-
Hamza Çalışıcı
and
Ergül Türkmen
Published/Copyright:
May 30, 2012
Abstract.
Let R be a ring and M a left R-module. An R-module N is called a cofinite extension of M in case 
and 
is finitely generated. We say that M has the propertyCE (resp. CEE) if M has a supplement (resp. ample supplements) in every cofinite extension. In this study we give various properties of modules with these properties. We show that a module M has the property CEE iff every submodule of M has the property CE. A ring R is semiperfect iff every left R-module has the property CE. We also study cofinitely injective modules, direct summands of every cofinite extension, as a generalization of injective modules.
Received: 2011-05-24
Revised: 2011-12-30
Published Online: 2012-05-30
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces
- Modules that have a supplement in every cofinite extension
- Boundary value problems of statics of the elastic mixture theory
- On grand Lorentz spaces and the maximal operator
- Measurable and nonmeasurable sets with homogeneous sections
- Complexifications of real spaces: General aspects
- Continuous Hu cohomology
- Convergence and existence results for best C-proximity points
- Aspects of slice stability in locale theory
- On the irreducibility of Hurwitz spaces of coverings with two special fibers
- Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions
