The Unitality of Quantum B-algebras
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.
KeywordsQuantale 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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