论文标题
半能分布l-型肌体
Semilinear idempotent distributive l-monoids
论文作者
论文摘要
我们证明了通过嵌套的总构造的完全有序的单型单体的表示定理。使用此表示定理，我们获得了各种半掌握分布式L-单子l-Onoids的副标理成员的表征，并证明了其次变量的晶格是无限的。对于多种交通型分布式L-键型的多种多样，我们对其亚变化的晶格进行了明确的描述，并表明其每个亚变量都是有限的公理。最后，我们给出了一个完全有序的单型跨度的跨度的表征，在完全有序的单体类别中具有汞合金，特别表明，完全有序的交换性型单体类别具有强大的合并性属性，并且各种类别的分布l-Monoid类别都没有合并的属性。我们还表明，恰好有七个非平凡的有限生成的亚属体，这些亚属性具有融合特性。我们能够确定其三个亚地区以外的所有属性是否具有合并财产。
We prove a representation theorem for totally ordered idempotent monoids via a nested sum construction. Using this representation theorem we obtain a characterization of the subdirectly irreducible members of the variety of semilinear idempotent distributive l-monoids and a proof that its lattice of subvarieties is countably infinite. For the variety of commutative idempotent distributive l-monoids we give an explicit description of its lattice of subvarieties and show that each of its subvarieties is finitely axiomatized. Finally we give a characterization of which spans of totally ordered idempotent monoids have an amalgam in the class of totally ordered monoids, showing in particular that the class of totally ordered commutative idempotent monoids has the strong amalgamation property and that various classes of distributive l-monoids do not have the amalgamation property. We also show that exactly seven non-trivial finitely generated subvarieties of the variety of semilinear idempotent distributive l-monoids have the amalgamation property; we are able to determine for all but three of its subvarieties whether they have the amalgamation property or not.
