%0 Journal Article
%A Ruiz Sancho, Jesús María
%T On pythagorean real irreducible algebroid curves
%D 1984
%@ 0035-7596
%U https://hdl.handle.net/20.500.14352/64761
%X 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.
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