General Mixed Lattices

IF 0.6 4区数学 Q3 MATHEMATICS

Order-A Journal on the Theory of Ordered Sets and Its Applications Pub Date : 2023-09-27 DOI:10.1007/s11083-023-09648-4

Jani Jokela

引用次数: 0

Abstract

Abstract 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. In particular, we establish the equivalence of the one-sided associative, distributive and modular laws in mixed lattices. 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.

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一般混合格

摘要混合格是由两个偏序的集合构成的格型结构，它推广了格的概念。混合晶格理论以前已经在各种代数结构中进行了研究，例如群和半群，而混合晶格的更一般的概念仍然没有被探索。本文研究了混合晶格的基本性质以及各种性质之间的关系。特别地，我们建立了混合格中单侧结合律、分配律和模律的等价性。我们还给出了混合格和混合格群作为满足一组公设的非交换非结合代数的另一种定义。然后证明代数定义和序理论定义是等价的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Order-A Journal on the Theory of Ordered Sets and Its Applications 数学-数学

CiteScore

1.10

自引率

25.00%

发文量

审稿时长

>12 weeks

期刊介绍： Order presents the most original and innovative research on ordered structures and the use of order-theoretic methods in graph theory and combinatorics, lattice theory and algebra, set theory and relational structures, and the theory of computing. In each of these categories, we seek submissions that make significant use of orderings to study mathematical structures and processes. The interplay of order and combinatorics is of particular interest, as are the application of order-theoretic tools to algorithms in discrete mathematics and computing. Articles on both finite and infinite order theory are welcome. The scope of Order is further defined by the collective interests and expertise of the editorial board, which are described on these pages. Submitting authors are asked to identify a board member, or members, whose interests best match the topic of their work, as this helps to ensure an efficient and authoritative review.