Families of local involutive integral residuated lattice-ordered commutative monoids admitting Boolean term

We present a family of local involutive integral bounded residuated lattice-ordered commutative monoids (involutive residuated lattices, for short) having Boolean term, radical term (see \cite{CT12} and \cite{T23}), and satisfying GAP (Generalized Appel property) (see \cite{T23}).The construction of this family is based in the examples given in \cite[Subsection 5.1]{CT12}, by taking $\text{bfm}\text{LLn}$ in place of $\text{bfm}{L}_{n+1}$ and $\text{bfm}{L}_{p+1}$ in place of the two element Boolean algebra. In some sense this paper is a companion of the paper \cite{T23}, in which the General Apple Property (GAP) and Boolean terms are studied.