  In this paper we study structural properties of residuated lattices that are
idempotent as monoids. We provide descriptions of the totally ordered members
of this class and obtain counting theorems for the number of finite algebras in
various subclasses. We also establish the finite embeddability property for
certain varieties generated by classes of residuated lattices that are
conservative in the sense that monoid multiplication always yields one of its
arguments. We then make use of a more symmetric version of Raftery's
characterization theorem for totally ordered commutative idempotent residuated
lattices to prove that the variety generated by this class has the amalgamation
property. Finally, we address an open problem in the literature by giving an
example of a noncommutative variety of idempotent residuated lattices that has
the amalgamation property.
