3 problems

Finite nuclear-image conjecture. The finite nuclear images of conuclear images of negative cones of $\ell$-groups are precisely the finite integral residuated lattices.

Nuclear-image conjecture. The nuclear images of sub-s$\ell$-monoids of negative cones of $\ell$-groups are precisely the integral s$\ell$-monoids.

Idempotency conjecture. Every parasemifield which is finitely generated as a semiring is additively idempotent.