Prime ideals in nilpotent Iwasawa algebras
Let G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of G, and use this to show that the prime spectrum of kG is a disjoint union of commutative strata. We...
| Egile nagusia: | |
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| Formatua: | Journal article |
| Hizkuntza: | English |
| Argitaratua: |
2011
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| _version_ | 1826292981454340096 |
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| author | Ardakov, K |
| author_facet | Ardakov, K |
| author_sort | Ardakov, K |
| collection | OXFORD |
| description | Let G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of G, and use this to show that the prime spectrum of kG is a disjoint union of commutative strata. We also show that every prime ideal of kG is completely prime. The key ingredient in the proof is the construction of a non-commutative valuation on certain filtered simple Artinian rings. |
| first_indexed | 2024-03-07T03:23:03Z |
| format | Journal article |
| id | oxford-uuid:b8144de9-49db-40cd-a7f9-fa406ceeb5e4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:23:03Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:b8144de9-49db-40cd-a7f9-fa406ceeb5e42022-03-27T04:53:29ZPrime ideals in nilpotent Iwasawa algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b8144de9-49db-40cd-a7f9-fa406ceeb5e4EnglishSymplectic Elements at Oxford2011Ardakov, KLet G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of G, and use this to show that the prime spectrum of kG is a disjoint union of commutative strata. We also show that every prime ideal of kG is completely prime. The key ingredient in the proof is the construction of a non-commutative valuation on certain filtered simple Artinian rings. |
| spellingShingle | Ardakov, K Prime ideals in nilpotent Iwasawa algebras |
| title | Prime ideals in nilpotent Iwasawa algebras |
| title_full | Prime ideals in nilpotent Iwasawa algebras |
| title_fullStr | Prime ideals in nilpotent Iwasawa algebras |
| title_full_unstemmed | Prime ideals in nilpotent Iwasawa algebras |
| title_short | Prime ideals in nilpotent Iwasawa algebras |
| title_sort | prime ideals in nilpotent iwasawa algebras |
| work_keys_str_mv | AT ardakovk primeidealsinnilpotentiwasawaalgebras |