##### Department of Mathematics,

University of California San Diego

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### Algebra seminar

## Sebastian Pardo Guerra

#### UC San Diego

## On the lattice of lattice preradicals and some isomorphic structures

##### Abstract:

Most algebraic structures can be given a lattice structure. For instance, any R-module defines a lattice where the meet and the join operations are given by the intersection and the sum of modules. Furthermore, any R-module morphism gives rise to a usual lattice morphism between the corresponding lattices. Actually, these two correspondences comprise a functor from the category of

R-modules to the category of complete modular lattices and usual lattice morphisms. However, this last category does not summon some basic algebraic properties that modules have (for example, the first theorem of isomorphism). With this in mind, we consider the category of linear modular lattices and linear morphisms, where we extend the notions of preradicals, and thus, describe the big lattice of lattice preradicals. In the process, we define some isomorphic structures to such lattice of lattice preradicals.

### November 20, 2023

### 2:00 PM

APM 7321

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