Geodesic
Honest submodules
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 225-241 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular some applications to the study and the structure theory of torsion modules are provided.
Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular some applications to the study and the structure theory of torsion modules are provided.
Classification : 16D80, 16W35
Keywords: closed submodules; honest submodules; topological filters 
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}
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Jara, Pascual. Honest submodules. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 225-241. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a18/

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