Amalgamation in classes of involutive commutative residuated lattices

The amalgamation property and its variants are in strong relationship with various syntactic interpolation properties of substructural logics, hence its investigation in varieties of residuated lattices is of particular interest. The amalgamation property is investigated in some classes of non-divisible, non-integral, and non-idempotent involutive commutative residuated lattices in this paper. It is proved that the classes of odd and even totally ordered, involutive, commutative residuated lattices fail the amalgamation property. It is also proved that their subclasses formed by their idempotent-symmetric algebras have the amalgamation property but fail the strong amalgamation property. Finally, it is shown that the variety of semilinear, idempotent-symmetric, odd, involutive, commutative residuated lattices has the amalgamation property, and hence also the transferable injections property