连通拓扑格序群

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2023-01-10 DOI:10.1007/s00012-022-00800-6

Francis Jordan

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引用次数: 0

摘要

我们回答了关于允许连通格序群拓扑的格序群的两个开放问题。我们证明，在一般情况下，承认连通格序群拓扑并不影响格序群的代数结构。例如，承认一个连通的格序群拓扑并不意味着格序群是阿基米德的，甚至是可表示的。另一方面，如果假设格序群有基，那么承认格序群拓扑意味着格序群是实数副本的次直积。

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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Connected topological lattice-ordered groups

We answer two open problems about lattice-ordered groups that admit a connected lattice-ordered group topology. We show that, in the general case, admitting a connected lattice-ordered group topology does not effect the algebraic structure of the lattice-ordered group. For example, admitting a connected lattice-ordered group topology does not imply that the lattice-ordered group is Archimedean or even representable. On the other hand, if one assumes that the lattice-ordered group has a basis, then admitting a lattice-ordered group topology implies that the lattice-ordered group is a subdirect product of copies of the real numbers.

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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.