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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19221 |
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| _version_ | 1866912620138725376 |
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| author | Grätzer, G. |
| author_facet | Grätzer, G. |
| contents | We continue the study of exponent-cancellation for finite ordered sets. It is known that $A$ can be reconstructed from $A^{A}$, from $(A^{A})^{A}$, and from $A^{A^{A}}$. In this note we prove the next result in this hierarchy: the ordered set $(A^{A^{A}})^{A^{A^{A}}}$ determines $A$ up to isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on the ordered set $A^A$. Part III. Exponent-cancellations Grätzer, G. Rings and Algebras 06 We continue the study of exponent-cancellation for finite ordered sets. It is known that $A$ can be reconstructed from $A^{A}$, from $(A^{A})^{A}$, and from $A^{A^{A}}$. In this note we prove the next result in this hierarchy: the ordered set $(A^{A^{A}})^{A^{A^{A}}}$ determines $A$ up to isomorphism. |
| title | Notes on the ordered set $A^A$. Part III. Exponent-cancellations |
| topic | Rings and Algebras 06 |
| url | https://arxiv.org/abs/2509.19221 |