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On pythagorean real irreducible algebroid curves

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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


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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
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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