3 problems

Let $R\le \overline{\mathbb{Q}}$ be a subring with finitely many units. An order conjecture. There exists an integer $d\in\mathbb{Z}_{<0}$ such that $R$ is an order in…

Let $(R,*)$ be a ring -ring, and let \overline\operatorname{Herm}(R,*) denote the Hermitian quotient associated with $(R,*)$. Freeness conjecture. For any ring -ring $(R,*)$,…

NIP conjecture for omega-categorical rings. Every $\omega$-categorical ring with NIP is nilpotent-by-finite.