Co-rotation-annihilations of residuated semigroups

Two new ways to construct involutive residuated semigroups are introduced in this paper, namely, connected and disconnected co-rotation-annihilations. Co-rotation-annihilations utilizes two particular kinds of residuated semigroups to construct a third one. The method is suitable for constructing a large class of examples of negative rank involutive FLeFLe-algebras, that is, where the unit element of the algebra is smaller than the falsum constant, which defines the involution in the algebra.