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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| Format: | Article |
| Language: | English |
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MDPI AG
2025-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/9/1407 |
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| author | Jorge P. Fatelo Nelson Martins-Ferreira |
| author_facet | Jorge P. Fatelo Nelson Martins-Ferreira |
| author_sort | Jorge P. Fatelo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2b2fc413be1e47a3b5e34ece09cda995 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-2b2fc413be1e47a3b5e34ece09cda9952025-08-20T02:24:49ZengMDPI AGMathematics2227-73902025-04-01139140710.3390/math13091407Reconstructing Classical Algebras via Ternary OperationsJorge P. Fatelo0Nelson Martins-Ferreira1School of Technology and Management, Polytechnic of Leiria, 2411-901 Leiria, PortugalSchool of Technology and Management, Polytechnic of Leiria, 2411-901 Leiria, PortugalAlthough 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.https://www.mdpi.com/2227-7390/13/9/1407Boolean algebrasMV-algebrasde Morgan algebrasternary operationsrings and near-rings of characteristic two |
| spellingShingle | Jorge P. Fatelo Nelson Martins-Ferreira Reconstructing Classical Algebras via Ternary Operations Mathematics Boolean algebras MV-algebras de Morgan algebras ternary operations rings and near-rings of characteristic two |
| title | Reconstructing Classical Algebras via Ternary Operations |
| title_full | Reconstructing Classical Algebras via Ternary Operations |
| title_fullStr | Reconstructing Classical Algebras via Ternary Operations |
| title_full_unstemmed | Reconstructing Classical Algebras via Ternary Operations |
| title_short | Reconstructing Classical Algebras via Ternary Operations |
| title_sort | reconstructing classical algebras via ternary operations |
| topic | Boolean algebras MV-algebras de Morgan algebras ternary operations rings and near-rings of characteristic two |
| url | https://www.mdpi.com/2227-7390/13/9/1407 |
| work_keys_str_mv | AT jorgepfatelo reconstructingclassicalalgebrasviaternaryoperations AT nelsonmartinsferreira reconstructingclassicalalgebrasviaternaryoperations |