MathDB3 problems
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Finite nuclear images of conuclear images of negative cones
Finite nuclear-image conjecture. The finite nuclear images of conuclear images of negative cones of -groups are precisely the finite integral residuated lattices.
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Nuclear images of sub-sℓ-monoids of negative cones
Nuclear-image conjecture. The nuclear images of sub-s-monoids of negative cones of -groups are precisely the integral s-monoids.
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The idempotency conjecture for finitely generated parasemifields
Idempotency conjecture. Every parasemifield which is finitely generated as a semiring is additively idempotent.