关于Fremlin的阿基米德-里兹空间张量积的两个结果

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2023-07-14 DOI:10.1007/s00012-023-00822-8

Gerard Buskes, Page Thorn

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引用次数: 4

摘要

在本文中，我们刻画了对于任何无穷基数\（\alpha\），两个阿基米德-里兹空间的Fremlin张量积（见Fremlin在Am J Math 94:777–7981972）何时是Dedekind\（\aalpha\）-完备的。我们还提供了阿基米德-里兹空间E中理想I的一个例子，使得I与自身的Fremlin张量积在E与自身的弗雷姆林张量积中不是理想。

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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Two results on Fremlin’s Archimedean Riesz space tensor product

In this paper, we characterize when, for any infinite cardinal \(\alpha \), the Fremlin tensor product of two Archimedean Riesz spaces (see Fremlin in Am J Math 94:777–798, 1972) is Dedekind \(\alpha \)-complete. We also provide an example of an ideal I in an Archimedean Riesz space E such that the Fremlin tensor product of I with itself is not an ideal in the Fremlin tensor product of E with itself.

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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.