Reconstructing Classical Algebras via Ternary Operations

Pereira Fatelo, Jorge; Martins-Ferreira, Nelson

http://hdl.handle.net/10400.8/13828

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Authors

Pereira Fatelo, Jorge

Martins-Ferreira, Nelson

Abstract(s)

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.

Description

Article number - 1407
This article belongs to the Section A: Algebra and Logic

Keywords

Boolean algebras MV-algebras de Morgan algebras Ternary operations Rings and near-rings of characteristic two

URI

http://hdl.handle.net/10400.8/13828

Citation

Fatelo, J.P.; MartinsFerreira, N. Reconstructing Classical Algebras via Ternary Operations. Mathematics 2025, 13, 1407. https:// doi.org/10.3390/math13091407