CATEGORY OF COMPLEMENTED MODULAR LATTICES

This paper introduces a category whose objects are comple-mented modular lattices and whose morphisms are normal mappings. Furthermore, we show that complemented modular lattices arising from the submodule lattices of semisimple modules naturally belong to this framework, where module homomorphisms induce linear normal map-pings between the associated lattices. This construction provides a categorical setting for complemented modular lattices and strengthens the connection between lattice theory, module theory, and the theory of normal categories.

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