On pythagorean real irreducible algebroid curves



Downloads per month over past year

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

[thumbnail of RuizSancho28.pdf]

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


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

Origin of downloads

Repository Staff Only: item control page