Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices

@article{Lomp2011FleurysSD,
  title={Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices},
  author={Christian Lomp and Ayşe Çiğdem {\"O}zcan},
  journal={Colloquium Mathematicum},
  year={2011},
  volume={124},
  pages={133-144}
}
Based on a lattice theoretical approach, we give a complete characterization of modules with Fleury’s spanning dimension. An example of a non-Artinian, non-hollow module satisfying this finiteness condition is constructed. Furthermore we introduce and characterize the dual notion of Fleury’s spanning dimension. 

References

SHOWING 1-10 OF 14 REFERENCES
Modules with Chain Conditions on Non-essential Submodules
Abstract We investigate when modules which satisfy the descending (respectively, ascending) chain condition on non-essential submodules are uniform or Artinian (respectively, Noetherian).
Lifting modules : supplements and projectivity in module theory
Basic notions.- Preradicals and torsion theories.- Decompositions of modules.- Supplements in modules.- From lifting to perfect modules.
Generalized Hopfian modules
A module is called generalized Hopfian (gH) if any of its surjective endomorphisms has a small kernel. Such modules are in a sense dual to weakly co-Hopfian modules that were defined and extensively
General Lattice Theory
I First Concepts.- 1 Two Definitions of Lattices.- 2 How to Describe Lattices.- 3 Some Algebraic Concepts.- 4 Polynomials, Identities, and Inequalities.- 5 Free Lattices.- 6 Special Elements.-
Generalized Fitting modules and rings
Abstract An R-module M is called strongly Hopfian (respectively strongly co-Hopfian) if for every endomorphism f of M the chain Ker f ⊆ Ker f 2 ⊆ ⋯ (respectively Im f ⊇ Im f 2 ⊇ ⋯ ) stabilizes. The
A dual to the Goldie ascending chain condition on direct sums of submodules
  • Bull. Calcutta Math. Soc
  • 1981
...
1
2
...