3 papers
math.LO2026
Definable rank, o-minimal groups, and Wiegold's problem
Annalisa Conversano
We show that an o-minimal structure M defines groups with infinite definable rank if and only if M defines some finite power of . If no interval of M is coun…
math.LO2025
A Jordan-Chevalley decomposition beyond algebraic groups
Annalisa Conversano
We prove a decomposition of definable groups in o-minimal structures generalizing the Jordan-Chevalley decomposition of linear algebraic groups. It follows that any definable linea…
math.LO2025
Ring theory in o-minimal structures
Annalisa Conversano
We develop a general ring theory in the o-minimal setting culminating in a description of all the definable rings in an arbitrary o-minimal structure. We show that every definably…