International Journal of Theoretical Physics

, Volume 57, Issue 5, pp 1582–1590 | Cite as

The Unitality of Quantum B-algebras

  • Shengwei Han
  • Xiaoting Xu
  • Feng Qin


Quantum B-algebras as a generalization of quantales were introduced by Rump and Yang, which cover the majority of implicational algebras and provide a unified semantic for a wide class of substructural logics. Unital quantum B-algebras play an important role in the classification of implicational algebras. The main purpose of this paper is to construct unital quantum B-algebras from non-unital quantum B-algebras.


Quantale Quantum B-algebra Unital quantum B-algebra 



We wish to express our sincere thanks to the anonymous referee for careful reading of the manuscript, and for useful suggestions and valuable comments which helped to improve the presentation of the results.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShaanxi Normal UniversityXi’anPeople’s Republic of China
  2. 2.College of Mathematics and Information ScienceJiangxi Normal UniversityNanchangPeople’s Republic of China

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