量子B-modules

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2022-02-15 DOI:10.1002/malq.202100029

Xia Zhang, Wolfgang Rump

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引用次数: 1

摘要

量子b代数是描述量子的剩余结构的部分有序代数。例子出现在代数逻辑、非交换算术和量子理论中。具有平凡偏序的量子b代数等价于一个群。本文介绍了一种相应的量子模的模拟。证明了每个量子b模都有一个单射包络，该包络是一个量子模。注入包络被明确地构造为一个补全，一个Dedekind和MacNeille补全的多偏序集版本。

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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Quantum B-modules

Quantum B-algebras are partially ordered algebras characterizing the residuated structure of a quantale. Examples arise in algebraic logic, non-commutative arithmetic, and quantum theory. A quantum B-algebra with trivial partial order is equivalent to a group. The paper introduces a corresponding analogue of quantale modules. It is proved that every quantum B-module admits an injective envelope which is a quantale module. The injective envelope is constructed explicitly as a completion, a multi-poset version of the completion of Dedekind and MacNeille.

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.