Rings of Algebraic Numbers in Infinite Extensions of $\Q$ and Elliptic Curves Retaining Their Rank

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129624We show that elliptic curves whose Mordell-Weil groups are finitely generated over some infinite extensions of $\Q$, can be used to show the Diophantine undecidability of the rings of integers and bigger rings contained in some infinite extensions of rational numbers.Number TheoryLogic11U05; 11G05Rings of Algebraic Numbers in Infinite Extensions of $\Q$ and Elliptic Curves Retaining Their Ranktext