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Quotient Quantum-Wajsberg Algebras
Lavinia Corina Ciungu
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.
Keywords: Quantum-Wajsberg algebra, q-deductive system, p-deductive system, deductive system, congruence, quotient quantum-Wajsberg algebra, weakly linearity, quasi-linearity
AMS classification (2020): 06F35, 03G25, 06A06, 81P10