The Artin--Rees lemma and size of spaces over nonassociative complete filtered rings
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913216645300224 |
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| author | Manoharmayum, Jayanta |
| author_facet | Manoharmayum, Jayanta |
| contents | This paper studies nonassociative filtered rings using associated gradations. We show that a complete filtered ring $R$ with affine associated graded ring generated in degree $1$ is a local ring, and prove that the Artin--Rees lemma holds for $R$. Assuming finiteness of the residue field, we derive asymptotics for abelian groups with an operation of $R$, and identify classes of torsion elements for spaces over a central extension of $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Artin--Rees lemma and size of spaces over nonassociative complete filtered rings Manoharmayum, Jayanta Rings and Algebras 17A01, 17A60, 17D99 This paper studies nonassociative filtered rings using associated gradations. We show that a complete filtered ring $R$ with affine associated graded ring generated in degree $1$ is a local ring, and prove that the Artin--Rees lemma holds for $R$. Assuming finiteness of the residue field, we derive asymptotics for abelian groups with an operation of $R$, and identify classes of torsion elements for spaces over a central extension of $R$. |
| title | The Artin--Rees lemma and size of spaces over nonassociative complete filtered rings |
| topic | Rings and Algebras 17A01, 17A60, 17D99 |
| url | https://arxiv.org/abs/2401.17508 |