Quotient quantum-Wajsberg algebras
Quantum Algebra
2024-05-01 v3
Abstract
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.
Cite
@article{arxiv.2304.01845,
title = {Quotient quantum-Wajsberg algebras},
author = {Lavinia Corina Ciungu},
journal= {arXiv preprint arXiv:2304.01845},
year = {2024}
}