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Ruiz Sancho, Jesús María
(1984)
*On pythagorean real irreducible algebroid curves.*
Rocky Mountain Journal of Mathematics, 14
(4).
pp. 899-901.
ISSN 0035-7596

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Official URL: http://projecteuclid.org/euclid.rmjm/1250127369

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Real irreducible algebroid curve; Pythagoras number; sum of squares; low multiplicity |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 20140 |

Deposited On: | 26 Feb 2013 18:49 |

Last Modified: | 12 Dec 2018 15:14 |

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