2023/04/04 by Lavinia Corina Ciungu, Ciungu, Lavinia Corina
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Quantum Algebra (math.QA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2304.01845
openalex publication_date 2023/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define and study the notions of q-deductive systems, p-deductive systems, deductive systems, maximal and strongly maximal q-deductive systems in quantum-Wajsberg algebras. We also introduce the notion of congruences induced by deductive systems of a quantum-Wajsberg algebra, and we show that there is a relationship between congruences and deductive systems. Furthermore, we define the quotient quantum-Wajsberg algebra with respect to a deductive system, and prove that the quotient quantum-Wajsberg algebra is locally finite if and only if the deductive system is strongly maximal. Finally, we define the weakly linear and quasi-linear quantum-Wajsberg algebras, and give a characterization of weakly linear quotient quantum-Wajsberg algebras.