On pythagorean real irreducible algebroid curves
| dc.contributor.author | Ruiz Sancho, Jesús María | |
| dc.date.accessioned | 2023-06-21T02:04:02Z | |
| dc.date.available | 2023-06-21T02:04:02Z | |
| dc.date.issued | 1984 | |
| dc.description.abstract | In this note we deal with the pythagoras number p of certain 1-dimensional rings, i.e., real irreducible algebroid curves over a real closed ground field k. The problem we are concerned with is to characterize those real irreducible algebroid curves which are pythagorean (i.e., p = 1). We obtain two theorems involving the value-semigroup. Then we apply them to solve the cases of: (a) Gorenstein curves, (b) planar curves, (c) monomial curves, and (d) curves of multiplicity <= 5. Finally, two conjectures are stated. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20140 | |
| dc.identifier.doi | 10.1216/RMJ-1984-14-4-899 | |
| dc.identifier.issn | 0035-7596 | |
| dc.identifier.officialurl | http://projecteuclid.org/euclid.rmjm/1250127369 | |
| dc.identifier.relatedurl | http://projecteuclid.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64761 | |
| dc.issue.number | 4 | |
| dc.journal.title | Rocky Mountain Journal of Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 901 | |
| dc.page.initial | 899 | |
| dc.publisher | Rocky Mountain Mathematics Consortium | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Real irreducible algebroid curve | |
| dc.subject.keyword | Pythagoras number | |
| dc.subject.keyword | sum of squares | |
| dc.subject.keyword | low multiplicity | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On pythagorean real irreducible algebroid curves | |
| dc.type | journal article | |
| dc.volume.number | 14 | |
| dcterms.references | A. Campillo, Algebroid curves in positive characteristic. Lecture Notes in Mathematics 813, Springer-Verlag, New York, 1980 S. Ebey, The classification of singular points of algebraic curves, Trans. A.M.S. 118 (1965), 454-471 E. Kunz, The value-semigroup of a one-dimensional Gorenstein rign. Proc. A.M.S. 25 (1970), 748-751 J. Lipman, Stable ideals and Arf rings, Amer. J. Math. 93 (1971), 649-685 J. M. Ruiz, Ph. D. Dissertation, Univ. Complutense de Madrid, 1982 J. M. Ruiz, On Pythagorean real curve germs, preprint, 1983 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 | |
| relation.isAuthorOfPublication.latestForDiscovery | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 |
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