Sup中的右代数与半单位量子和半积分量子的拓扑表示，再论

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2024-05-28 DOI:10.1515/ms-2024-0020

Javier Gutiérrez García, Ulrich Höhle

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引用次数: 0

摘要

让𝔔 是一个没有零除数的左侧且左稳定的简化量子。本文展示了如何系统地使用 2 的 "量子化"，将其视为𝔔 的规则而严格的右𝔔 子代数，从而既加强又简化了原论文[3]中针对半空量子和半积分量子给出的相当复杂的量子丰富拓扑结构。这一新构造的基础结构是半空量子、半积分量子和量子化拓扑空间的对偶范畴之间的邻接情况。

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Right algebras in Sup and the topological representation of semi-unital and semi-integral quantales, revisited

Let 𝔔 be a reduced left-sided and left-stable quantale without zero divisors. This paper shows how the systematic use of the «quantization» of 2 viewed as a regular and strict right 𝔔-subalgebra of 𝔔 can both strengthen and simplify the rather complicated construction of quantale-enriched topologies given for semi-unital and semi-integral quantales in the original paper [3]. The underlying structure for this new construction is an adjoint situation between the dual category of semi-unital, semi-integral quantales and quantized topological spaces.

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.