On Chains of prime ideals in ring of semialgebraic funtions
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.date.accessioned | 2023-06-19T13:27:33Z | |
| dc.date.available | 2023-06-19T13:27:33Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | In this work, we study the structure of non-refinable chains of prime ideals in the (real closed) rings S(M) and S*(M) of semialgebraic and bounded semialgebraic functions on a semialgebraic set M subset of R-m. We pay special attention to the prime z-ideals of S(M) and the minimal prime ideals of both rings. For the last, a decomposition of each semialgebraic set as an irredundant finite union of closed pure dimensional semialgebraic subsets plays a crucial role. We prove moreover the existence of maximal ideals in the ring S(M) of prefixed height whenever M is non-compact. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish GR | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/28164 | |
| dc.identifier.doi | 10.1093/qmath/hat048 | |
| dc.identifier.issn | 0033-5606 | |
| dc.identifier.officialurl | http://qjmath.oxfordjournals.org/content/65/3/893.abstract | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33760 | |
| dc.issue.number | 3 | |
| dc.journal.title | Quaterly journal of mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 930 | |
| dc.page.initial | 893 | |
| dc.publisher | Oxford univ press | |
| dc.relation.projectID | MTM2011-22435 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Semialgebraic function | |
| dc.subject.keyword | Zariski spectrum | |
| dc.subject.keyword | Maximal spectrum | |
| dc.subject.keyword | Real closed ring | |
| dc.subject.keyword | semialgebraic compactication | |
| dc.subject.keyword | Chain of prime ideals | |
| dc.subject.keyword | Maximal ideal | |
| dc.subject.keyword | Minimal prime ideal | |
| dc.subject.keyword | Z-ideal | |
| dc.subject.keyword | Semialgebraic depth | |
| dc.subject.keyword | Family of bricks | |
| dc.subject.keyword | Local compactness | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On Chains of prime ideals in ring of semialgebraic funtions | |
| dc.type | journal article | |
| dc.volume.number | 65 | |
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| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 499732d5-c130-4ea6-8541-c4ec934da408 | |
| relation.isAuthorOfPublication.latestForDiscovery | 499732d5-c130-4ea6-8541-c4ec934da408 |
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