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Ruiz Sancho, Jesús María (1984) On pythagorean real irreducible algebroid curves. Rocky Mountain Journal of Mathematics, 14 (4). pp. 899901. ISSN 00357596

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Official URL: http://projecteuclid.org/euclid.rmjm/1250127369
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Abstract
In this note we deal with the pythagoras number p of certain 1dimensional 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 valuesemigroup. 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 

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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