Reconstructing Classical Algebras via Ternary Operations

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 is...

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Bibliographic Details
Main Authors: Jorge P. Fatelo, Nelson Martins-Ferreira
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/9/1407
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Summary: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.
ISSN:2227-7390