december 2023 Implicative-orthomodular algebras
Lavinia Corina Ciungu
Bull. Belg. Math. Soc. Simon Stevin 30(4): 510-531 (december 2023). DOI: 10.36045/j.bbms.230508

Abstract

Starting from involutive BE algebras, we redefine the orthomodular algebras, by introducing the notion of implicative-orthomodular algebras. We investigate properties of implicative-orthomodular algebras, and give characterizations of these algebras. Then we define and study the notions of filters and deductive systems, and characterize certain classes of filters. Furthermore, we introduce and characterize the commutative deductive systems in implicative-orthomodular algebras. We also show that any deductive system determines a congruence, and conversely, for any congruence we can define a deductive system in an implicative-orthomodular algebra. We define the quotient implicative-orthomodular algebra with respect to the congruence induced by a deductive system, and prove that a deductive system is commutative if and only if all deductive systems of the corresponding quotient algebra are commutative.

Citation

Download Citation

Lavinia Corina Ciungu. "Implicative-orthomodular algebras." Bull. Belg. Math. Soc. Simon Stevin 30 (4) 510 - 531, december 2023. https://doi.org/10.36045/j.bbms.230508

Information

Published: december 2023
First available in Project Euclid: 31 December 2023

Digital Object Identifier: 10.36045/j.bbms.230508

Subjects:
Primary: 03G25 , 06A06 , 06F35 , 81P10
Secondary: 06C15

Keywords: congruence , deductive system , filter‎ , Implicative-orthomodular algebra , quantum-Wajsberg algebra

Rights: Copyright © 2023 The Belgian Mathematical Society

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.30 • No. 4 • december 2023
Back to Top