Reconstructing Classical Algebras via Ternary Operations
Rings and Algebras
2024-10-31 v1
Abstract
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a ternary operation. We demonstrate that these structures are isomorphic to various significant algebraic systems, including Boolean algebras, de Morgan algebras, MV-algebras, and (near) rings of characteristic two. Our work highlights the versatility of ternary operations in describing and connecting diverse algebraic structures.
Cite
@article{arxiv.2410.22345,
title = {Reconstructing Classical Algebras via Ternary Operations},
author = {Jorge Fatelo and Nelson Martins-Ferreira},
journal= {arXiv preprint arXiv:2410.22345},
year = {2024}
}