A Ring structure on the Class of Combinatorial Games
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914520920752128 |
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| author | Altman, Harry Lipparini, Paolo |
| author_facet | Altman, Harry Lipparini, Paolo |
| contents | J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. However, Conway product is not well defined on equivalence classes of arbitrary games (though it is well defined for surreals).
We consider an equivalence relation finer than Conway's and show that under such a relation combinatorial games actually form a Ring. We hint to other possible relations on the Class of combinatorial games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27847 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Ring structure on the Class of Combinatorial Games Altman, Harry Lipparini, Paolo Combinatorics Rings and Algebras 91A46, 13F70, 00A30 J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. However, Conway product is not well defined on equivalence classes of arbitrary games (though it is well defined for surreals). We consider an equivalence relation finer than Conway's and show that under such a relation combinatorial games actually form a Ring. We hint to other possible relations on the Class of combinatorial games. |
| title | A Ring structure on the Class of Combinatorial Games |
| topic | Combinatorics Rings and Algebras 91A46, 13F70, 00A30 |
| url | https://arxiv.org/abs/2604.27847 |