Reconstructing Classical Algebras via Ternary Operations
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929567277514752 |
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| author | Fatelo, Jorge Martins-Ferreira, Nelson |
| author_facet | Fatelo, Jorge Martins-Ferreira, Nelson |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstructing Classical Algebras via Ternary Operations Fatelo, Jorge Martins-Ferreira, Nelson Rings and Algebras 06E05, 06D30, 06D35, 03G25 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. |
| title | Reconstructing Classical Algebras via Ternary Operations |
| topic | Rings and Algebras 06E05, 06D30, 06D35, 03G25 |
| url | https://arxiv.org/abs/2410.22345 |