On pythagorean real irreducible algebroid curves
type: Item
instance of: scholarly article
title: On pythagorean real irreducible algebroid curves
zbMATH Open document ID: 0575.14020
DOI: 10.1216/RMJ-1984-14-4-899
published in: Rocky Mountain Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: A real irreducible algebroid curve A is a real complete local integral domain of dimension 1 with residue field a real closed field K. The Pythagoras number of A, pA, is the least p such that any sum of squares in A is a sum of p squares. A is called pythagorean if \(pA=1.\) In this note the author sketches the proof of two theorems characterizing pythagorean real algebroid curves in term of the valuation semi-group of their normalization. Several consequences are indicated, particularly results characterizing pythagorean real algebroid curves of low multiplicity.
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 11P05
zbMATH DE Number: 3918542
zbMATH Keywords: real irreducible algebroid curve
zbMATH Keywords: Pythagoras number
zbMATH Keywords: sum of squares
zbMATH Keywords: low multiplicity
author: Jesús M. Ruiz
reviewed by: Marie-Françoise Roy
MaRDI profile type: Publication
Wikidata QID: Q114060184
full work available at URL: rmj-1984-14-4-899
OpenAlex ID: W1988616638
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description: scientific article; zbMATH DE number 3918542