Via an encoding of the Modified Post’s Correspondence Problem, this paper shows that it is undecidable whether an automatic semigroup is cancellative.

Given a set-theoretic solution (X, r) of the Yang–Baxter equation, we denote by M = M(X, structure monoid and A A(X, r), respectively A0 left, right, derived r). It is shown that there exist left action on right 1-cocycles π 0 with coefficients in respect to these actions, respectively. We investigate when are injective, surjective, or bijective. In case X finite, it turns out bijective if only...

Starting from a decomposition result of MTL-chains as ordinal sums, we focus our attention on a particular kind of indecomposable semihoops, namely weakly cancellative semihoops. Weak cancellation property is proved to be the difference between cancellation and pseudocomplementation, so it gives a new axiomatization of Product logic and ΠMTL. By adding this property, some new fuzzy logics (prop...