论文标题
结构定理的基于残留的晶格
Structure theorems for idempotent residuated lattices
论文作者
论文摘要
在本文中，我们研究了残留的晶格的结构特性，这些特性是单型的。我们提供了该类别的完全有序成员的描述，并获得了各种子类中有限代数数量的计数定理。我们还建立了由残留的晶格类别生成的某些品种的有限嵌入性能，这些品种是保守的，因为Monoid乘法始终会产生其参数之一。然后，我们利用Raftery的表征定理的更对称版本的完全有序的交换性依从性残留的晶格来证明该类别产生的品种具有合并属性。最后，我们通过举例说明具有合并属性的各种依恋型残留晶格的示例来解决文献中的一个空旷问题。
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.
