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Cocompact lattices. (English) Zbl 0855.06007
Summary: A lattice \(L\) is called cocompact if its dual \(L^0\) is compact. If \(M\) is an \(R\)-module, the lattice \(S_R (M)\) of all the submodules of \(M\) is cocompact iff \(M\) is finitely cogenerated. Most of the properties of these modules are proved in the general lattice setting.
MSC:
06C05 Modular lattices, Desarguesian lattices
06C20 Complemented modular lattices, continuous geometries
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