A constructive counterpart of the subdirect representation theorem for reduced rings
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913471007817728 |
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| author | Kuroki, Ryota |
| author_facet | Kuroki, Ryota |
| contents | We give a constructive counterpart of the theorem of Andrunakievič and Rjabuhin, which states that every reduced ring is a subdirect product of domains. As an application, we extract a constructive proof of the fact that every ring $A$ satisfying $\forall x\in A. x^3=x$ is commutative from a classical proof. We also prove a similar result for semiprime ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A constructive counterpart of the subdirect representation theorem for reduced rings Kuroki, Ryota Rings and Algebras 16D70 (Primary) 16N60, 16U80, 16Z05, 03F65 (Secondary) We give a constructive counterpart of the theorem of Andrunakievič and Rjabuhin, which states that every reduced ring is a subdirect product of domains. As an application, we extract a constructive proof of the fact that every ring $A$ satisfying $\forall x\in A. x^3=x$ is commutative from a classical proof. We also prove a similar result for semiprime ideals. |
| title | A constructive counterpart of the subdirect representation theorem for reduced rings |
| topic | Rings and Algebras 16D70 (Primary) 16N60, 16U80, 16Z05, 03F65 (Secondary) |
| url | https://arxiv.org/abs/2408.09222 |