Four New Construction Methods on Residuated Monoids

Varieties of commutative residuated lattices are algebraic counterparts of extensions of the substructural logic FLe. We present four new construction methods that result in involutive commutative residuated monoids, namely, connected co-rotation, connected and disconnected co-rotation-annihilation, and the involutive ordinal sums construction. All constructions are suitable for constructing nonpositive rank FLe-algebras. The last one is suitable for constructing new zero-rank (that is, group-like) FLe-algebras from a family of such algebras.