On pythagorean real irreducible algebroid curves
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...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1984 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/64761 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/64761 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.7 Real irreducible algebroid curve Pythagoras number sum of squares low multiplicity Geometria algebraica 1201.01 Geometría Algebraica |
| Sumario: | 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. |
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