Undefinability of min-conjunction in MTL

Firstly, a sufficient and necessary condition is given to decide whether the lattice operations of a WNM-chain can be definable from its other operations. Secondly, we show that it is indeed necessary to introduce the min-conjunction into MTL as a primitive connective by constructing a left-continuous t-norm such that in the propositional calculus defined by this t-norm the min-conjunction and max-disjunction are not definable from the strong conjunction, implication and truth constant .