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.

在本文中，我们研究了等幂作为等分体的剩余格的结构性质。我们提供了此类的全序成员的描述，并获得了各个子类中有限代数数量的计数定理。我们还建立了由残差格类生成的某些变体的有限可嵌入性，这些残差格是保守的，在这种意义上，等分面乘法总是产生其参数之一。然后，我们将Raftery刻画定理的一个更为对称的形式用于完全有序的交换幂等残差格，以证明此类所产生的变种具有合并特性。最后，