Reconstructing Classical Algebras via Ternary Operations

Jorge P. Fatelo () and Nelson Martins-Ferreira
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Jorge P. Fatelo: School of Technology and Management, Polytechnic of Leiria, 2411-901 Leiria, Portugal
Nelson Martins-Ferreira: School of Technology and Management, Polytechnic of Leiria, 2411-901 Leiria, Portugal

Mathematics, 2025, vol. 13, issue 9, 1-17

Abstract: Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified using 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.

Keywords: Boolean algebras; MV-algebras; de Morgan algebras; ternary operations; rings and near-rings of characteristic two (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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