 Noncommutative Algebras
PseudoBCK Algebras versus mpseudoBCK Algebras
Afrodita Iorgulescu
This monograph is devoted mainly to the author’s results in her research on noncommutative algebras related to logic started on October 17, 2022, results never published.
It would not be written in so little time and with so many important results and examples without the help of the computer program Prover9Mace4, developed by William W. McCune (1953 – 2011).
There exist a framework of noncommutative algebras of logic, having in its `center' the pseudoBCK algebra.
In this monograph, the author mainly has generalized to the noncommutative case the mBCK algebra and its related algebras, as particular cases of unital magmas, thus creating a new framework of noncommutative algebras, having in its `center' the new mpseudoBCK algebra. The pseudoMV algebras are particular cases of mpseudoBCK algebras, the groups belong to this new framework.
But, the goal of her research was to define and study the quantumpseudoMV algebra, the noncommutative generalization of quantumMV algebra. She was able to reach her goal only because she has discovered the `principle' that governs the noncommutative algebras, called `transposition' principle (`mtransposition' principle, for magmas).
She has also introduced and studied other noncommutative generalizations of quantum algebras: the bounded involutive pseudolattices, the {bf pseudoDe Morgan algebras} and the orthopseudolattices.
The book has 18 chapters, divided into three parts: Part I (centered on pseudoBCK algebras: Chapters 1 – 7), Part II (the core of the monograph, centered on mpseudoBCK algebras: Chapters 8 – 16) and Part III (`bridge' theorems: Chapters 17, 18).
July 2024
9781848904637
