Geodesic
Construction of unital quantales
Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 761-776

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DOI

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.
DOI : 10.4153/S0008439525000104
Mots-clés : Quantale, unital quantale, unitally non-distributive quantale 
Han, Shengwei; Lv, Jiaxin. Construction of unital quantales. Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 761-776. doi: 10.4153/S0008439525000104
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     title = {Construction of unital quantales},
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     year = {2025},
     volume = {68},
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     doi = {10.4153/S0008439525000104},
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