The idiomatic content of module theory: Some uses

Autor: Luis Angel Zaldívar Corichi
Idioms, upper-continuos modular lattices are in somehow the order analogy of module theory, in fact the point-free theory of idioms (inflators and nuclei) can be applied to module categories as a localizations gadgets, that is to say, the nuclei on the idiom of left ideals of a ring controls the localizations of the module category, thus many situations of idioms (and frames) have an theoretic impact in the study of ring theory and module theory. This time we will see the boolean and spatial aspects of this theory and how these are related with the behaviour of the module category (and the ring) in play.