2 problems

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

Conjecture on residual self-quotients. Conditions involving terms of the form $x\backslash x$ and $x\slash x$ should provide a more satisfying account of the role of a multiplicati…