Local Bézout Theorem — Paper Nexus

Summary

It is proved that there are finitely many zeroes of the system above the residual zero of the Henselian local domain, (V,m,k), and the sum of their multiplicities is r.

Keywords

Mathematics, Multiplicity (mathematics), Elementary proof, Discrete mathematics, Residual

References

Anneaux locaux henséliensMichel Raynaud — 1970
Real algebraic geometryBochnak, Jacek 1943-, Coste, Michel 1950-, Roy, Marie-Françoise 1950- — 1992
The Basic Theory of Power SeriesJesús M. Ruíz — 1993
A computational model for algebraic power seriesMaría Emilia Alonso García, Teo Mora, Mario Di Raimondo — 1992
Singularities of differentiable mapsVladimir I. Arnold, Gusejn-Zade, Sabir M., Varčenko, Aleksandr N. 1949- — 2018
Singularities of differentiable maps正志池, 正人辻井 — 1987
EFFECTIVE ALGEBRAIC POWER SERIESM. Alonso, F. Castro-Jiménez, H. Hauser — 2005
Analytic Functions of Several Complex Variables.J. W. Gray, Robert C. Gunning, Hugo Rossi — 1968
Commutative ring theory: Regular ringsH. Matsumura, M. Reid — 1987
Analytic functions of several complex variablesN. Bogolubov, A. Logunov, A. Oksak — 1965
An Algorithm to Compute the Equations of Tangent ConesFerdinando Mora — 1982
A New Criterion for Normal Form AlgorithmsB. Mourrain — 1999

Cited by

Local Bézout theorem for Henselian ringsM. Emilia Alonso, Henri Lombardi — 2015
A henselian preparation theoremLaurent Moret-Bailly — 2021
A Topological Approach to the Bézout' Theorem and Its FormsSusmit Bagchi — 2023

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