An Independent Set of Axioms of MV-Algebras and Solutions of the Set-Theoretical Yang–Baxter Equation

Abstract

The aim of this paper is to give a new equivalent set of axioms for MV-algebras, and to show that the axioms are independent. In addition to this, we handle Yang-Baxter equation problem. In conclusion, we construct a new set-theoretical solution for the Yang-Baxter equation by using MV-algebras.

Unification Theories: Means and Generalized Euler Formulas

“…As we continued our work on unification theories begun in previous papers (see, for example, [2,4,7,9,10]), the unification approaches led us to new results. The Yang-Baxter equation (see [11][12][13][14]) can be interpreted in terms of logical circuits and, in logic, it represents a kind of compatibility condition when working with many logical sentences at the same time. In this type of logic, we work at the same time with sentences that contradict each other.…”

Mathematics and Poetry • Unification, Unity, Union

“…The sections of the current paper contain not only examples of unification structures in mathematics, but also various versions of the Yang-Baxter equation. This paper could be extended to a discussion about Logic [32][33][34], Machine Learning [35,36], transcendence and transcendental numbers [23,37], transdisciplinarity [38][39][40], etc.…”

On Transcendental Numbers: New Results and a Little History

“…In some special issues on Hopf algebras, quantum groups and Yang-Baxter equations, several papers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], as well the feature paper [23], covered many topics related to the Yang-Baxter equation, ranging from mathematical physics to Hopf algebras, from Azumaya Monads to quantum computing, and from Mathematical Logic to Rota-Baxter equations.…”