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Construction of unital quantales

Part of: Ordered structures Ordered sets Lattices

Published online by Cambridge University Press:  30 January 2025

Shengwei Han  and
Jiaxin Lv
Shengwei Han*
Affiliation:
Department of Mathematics, Shaanxi Normal University, Xi’an, 710119, China lvjiaxin@snnu.edu.cn
Jiaxin Lv
Affiliation:
Department of Mathematics, Shaanxi Normal University, Xi’an, 710119, China lvjiaxin@snnu.edu.cn
*
e-mail: hansw@snnu.edu.cn
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Abstract

Unital quantales constitute a significant subclass within quantale theory, which play a crucial role in the theoretical framework of quantale research. The main purpose of this article is to investigate the construction of unital quantales from a given quantale. Using Q-algebras, we prove that every quantale is embedded into a unital quantale, which generalizes the work of Paseka and Kruml for the construction of unital quantales. Based on which, we further show that every quantale can be transformed into a unitally non-distributive quantale, which expands the foundational work of Guriérrez García and Höhle for unitally non-distributive quantales. Finally, we provide a variety of methods for constructing unital quantales from some special quantales.

Keywords

Quantaleunital quantaleunitally non-distributive quantale

MSC classification

Primary: 06F07: Quantales 06A06: Partial order, general 06B05: Structure theory
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 16
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12471436 and 12331016).

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