Boolean rigs

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2025-09-12 DOI:10.1007/s00012-025-00904-9

Daniel Misselbeck-Wessel, Iosif Petrakis

引用次数: 0

Abstract

Semirings of partial Boolean-valued functions arise in Bishop’s approach to constructive measure theory. In this paper, we treat such semirings axiomatically. Lifting the corresponding result for Boolean rings, we prove a representation theorem à la Stone that aligns with the intended semantics. Moreover, among the semirings at hand, we determine the order of those that are free over finitely many generators.

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布尔钻井平台

部分布尔值函数的半环出现在Bishop的构造测度理论中。在本文中，我们公理化地处理这种半环。提升布尔环的相应结果，我们证明了一个与预期语义一致的表示定理 la Stone。此外，在现有的半环中，我们确定了在有限多个生成器上自由的半环的顺序。

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.