RT Journal Article
T1 On pythagorean real irreducible algebroid curves
A1 Ruiz Sancho, Jesús María
AB 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.
PB Rocky Mountain Mathematics Consortium
SN 0035-7596
YR 1984
FD 1984
LK https://hdl.handle.net/20.500.14352/64761
UL https://hdl.handle.net/20.500.14352/64761
LA eng
NO A. Campillo, Algebroid curves in positive characteristic. Lecture Notes in Mathematics 813, Springer-Verlag, New York, 1980S. Ebey, The classification of singular points of algebraic curves, Trans. A.M.S. 118 (1965), 454-471E. Kunz, The value-semigroup of a one-dimensional Gorenstein rign. Proc. A.M.S. 25 (1970), 748-751J. Lipman, Stable ideals and Arf rings, Amer. J. Math. 93 (1971), 649-685J. M. Ruiz, Ph. D. Dissertation, Univ. Complutense de Madrid, 1982J. M. Ruiz, On Pythagorean real curve germs, preprint, 1983
DS Docta Complutense
RD 1 may 2024