Chains conditions in algebraic lattices

TL;DR

This paper explores how the structure of chains in algebraic lattices relates to the order of their compact elements, providing new insights into their internal organization.

Contribution

It offers a detailed analysis of the connection between chains in algebraic lattices and the order structure of compact elements, with collaborative results across four chapters.

Findings

Characterization of chain conditions in algebraic lattices

Relationships between lattice chains and compact element orderings

New criteria for chain conditions in algebraic lattices

Abstract

This work studies the relationship between the chains of an algebraic lattice and the order structure of the join-semilattice of its compact elements. The results are presented into four chapters, each corresponding to a paper written in collaboration with Maurice Pouzet.