Given a residuated lattice L, we prove that the subset M V (L) of complement elements x * of L generates an M V -algebra if, and only if L is semi-divisible. Riečan states on a semi-divisible residuated lattice L, and Riečan states on M V (L) are essentially the very same thing. The same holds for Bosbach states as far as L is divisible. There are semi-divisible residuated lattices that do not have Bosbach states.
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