Year: 2025
Type: article
Abstract: In this paper, involutive weak exchange algebras (for short, involutive WE algebras) are introduced and studied. Their properties and characterizations are investigated. Some important results and examples are given. In particular, it is proven that in involutive WE algebras, the properties (BB), (B), (*), (**) and (Tr) are equivalent. Moreover, involutive BE, involutive GE, involutive pre-BCK and involutive pre-Hilbert algebras are considered, their connections are established. It is shown that involutive WE algebras (respectively, involutive GE algebras) satisfying the commutative property are Wajsberg algebras (respectively, Boolean algebras). Finally, the interrelationships between the classes of involutive algebras considered here are presented.
Source: Bulletin of the Section of Logic
Author: Andrzej Walendziak
Institution: University of Siedlce
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416952699