Computability of dimension groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911138495594496 |
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| author | Sabitova, Maria |
| author_facet | Sabitova, Maria |
| contents | We investigate the computability of the isomorphism set $\operatorname{Iso}(G_A,G_B)$ between $G_A$ and $G_B$, where $G_A$ is a subgroup of $\mathbb{Q}^n$ generated by columns of integer powers of a non-singular $n \times n$-matrix $A$ with integer entries. Assuming that the characteristic polynomial of $A$ is irreducible -- and under an additional condition when $n$ is not prime -- we prove that $\operatorname{Iso}(G_A,G_B)$ is computable; that is, there exists an algorithm that determines the structure in finitely many steps. We also present illustrative examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computability of dimension groups Sabitova, Maria Logic We investigate the computability of the isomorphism set $\operatorname{Iso}(G_A,G_B)$ between $G_A$ and $G_B$, where $G_A$ is a subgroup of $\mathbb{Q}^n$ generated by columns of integer powers of a non-singular $n \times n$-matrix $A$ with integer entries. Assuming that the characteristic polynomial of $A$ is irreducible -- and under an additional condition when $n$ is not prime -- we prove that $\operatorname{Iso}(G_A,G_B)$ is computable; that is, there exists an algorithm that determines the structure in finitely many steps. We also present illustrative examples. |
| title | Computability of dimension groups |
| topic | Logic |
| url | https://arxiv.org/abs/2509.04350 |