论文标题
一般混合格
General mixed lattices
论文作者
论文摘要
混合晶格是一个晶格型结构，该结构由带有两个部分订购的集合组成，并概括了晶格的概念。混合晶格理论先前已经在各种代数结构（例如组和半群）中进行了研究，而混合晶格的更一般的概念仍未得到探索。在本文中，我们研究了混合晶格的基本特性以及各种属性之间的关系，例如单方面的关联，分布和模块化定律。我们还提供了混合晶格和混合晶格基团的替代定义，作为满足某些假设集的非共同和非缔合代数。然后，代数和秩序理论定义是等效的。
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and semigroups, while the more general notion of a mixed lattice remains unexplored. In this paper, we study the fundamental properties of mixed lattices and the relationships between the various properties, such as the one-sided associative, distributive and modular laws. We also give an alternative definition of mixed lattices and mixed lattice groups as non-commutative and non-associative algebras satisfying a certain set of postulates. The algebraic and the order-theoretic definitions are then shown to be equivalent.
