On k-ary parts of maximal clones

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2024-03-18 DOI:10.1007/s00012-024-00851-x

引用次数: 0

Abstract

The main problem of clone theory is to describe the clone lattice for a given basic set. For a two-element basic set this was resolved by E.L. Post, but for at least three-element basic set the full structure of the lattice is still unknown, and the complete description in general is considered to be hopeless. Therefore, it is studied by its substructures and its approximations. One of the possible directions is to examine k-ary parts of the clones and their mutual inclusions. In this paper we study k-ary parts of maximal clones, for \(k\geqslant 2,\) building on the already known results for their unary parts. It turns out that the poset of k-ary parts of maximal clones defined by central relations contains long chains.

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关于最大克隆的 kary 部分

摘要克隆理论的主要问题是描述给定基本集的克隆点阵。对于二元素基本集，E.L. 波斯特已经解决了这个问题，但对于至少三元素基本集，克隆点阵的完整结构仍然是未知的，而且一般认为完全描述克隆点阵是没有希望的。因此，我们通过其子结构和近似结构对其进行研究。其中一个可能的方向是研究克隆的 kary 部分及其相互包含。在本文中，我们以已知的单元部分的结果为基础，研究了最大克隆的 k 元部分（k\geqslant 2,\）。结果证明，由中心关系定义的最大克隆的 kary 部分的集合包含长链。

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

Algebra Universalis 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3 months

期刊介绍： Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.