Primeness, semiprimeness and localisation in Iwasawa algebras
Necessary and sufficient conditions are given for the completed group algebras of a compact p-adic analytic group with coefficient ring the p-adic integers or the field of p elements to be prime, semiprime and a domain. Necessary and sufficient conditions for the localisation at semiprime ideals rel...
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1826264025478987776 |
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| author | Ardakov, K Brown, K |
| author_facet | Ardakov, K Brown, K |
| author_sort | Ardakov, K |
| collection | OXFORD |
| description | Necessary and sufficient conditions are given for the completed group algebras of a compact p-adic analytic group with coefficient ring the p-adic integers or the field of p elements to be prime, semiprime and a domain. Necessary and sufficient conditions for the localisation at semiprime ideals related to the augmentation ideals of closed normal subgroups are found. Some information is obtained about the Krull and global dimensions of the localisations. The results extend and complete work of A. Neumann and J. Coates et al. |
| first_indexed | 2024-03-06T20:01:11Z |
| format | Journal article |
| id | oxford-uuid:27587a1c-1f35-49c3-88d1-20cd9785815a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:01:11Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:27587a1c-1f35-49c3-88d1-20cd9785815a2022-03-26T12:06:26ZPrimeness, semiprimeness and localisation in Iwasawa algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:27587a1c-1f35-49c3-88d1-20cd9785815aEnglishSymplectic Elements at Oxford2004Ardakov, KBrown, KNecessary and sufficient conditions are given for the completed group algebras of a compact p-adic analytic group with coefficient ring the p-adic integers or the field of p elements to be prime, semiprime and a domain. Necessary and sufficient conditions for the localisation at semiprime ideals related to the augmentation ideals of closed normal subgroups are found. Some information is obtained about the Krull and global dimensions of the localisations. The results extend and complete work of A. Neumann and J. Coates et al. |
| spellingShingle | Ardakov, K Brown, K Primeness, semiprimeness and localisation in Iwasawa algebras |
| title | Primeness, semiprimeness and localisation in Iwasawa algebras |
| title_full | Primeness, semiprimeness and localisation in Iwasawa algebras |
| title_fullStr | Primeness, semiprimeness and localisation in Iwasawa algebras |
| title_full_unstemmed | Primeness, semiprimeness and localisation in Iwasawa algebras |
| title_short | Primeness, semiprimeness and localisation in Iwasawa algebras |
| title_sort | primeness semiprimeness and localisation in iwasawa algebras |
| work_keys_str_mv | AT ardakovk primenesssemiprimenessandlocalisationiniwasawaalgebras AT brownk primenesssemiprimenessandlocalisationiniwasawaalgebras |