About: AF+BG theorem

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In algebraic geometry the AF+BG theorem (also known as Max Noether's fundamental theorem) is a result of Max Noether that asserts that, if the equation of an algebraic curve in the complex projective plane belongs locally (at each intersection point) to the ideal generated by the equations of two other algebraic curves, then it belongs globally to this ideal.

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rdf:type	yago:WikicatTheoremsInAlgebra yago:WikicatTheoremsInAlgebraicGeometry yago:WikicatTheoremsInComplexGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	AF+BG theorem (en) Théorème AF+BG (fr) Теорема AF+BG (ru)
rdfs:comment	In algebraic geometry the AF+BG theorem (also known as Max Noether's fundamental theorem) is a result of Max Noether that asserts that, if the equation of an algebraic curve in the complex projective plane belongs locally (at each intersection point) to the ideal generated by the equations of two other algebraic curves, then it belongs globally to this ideal. (en) Теорема AF + BG (известная также как фундаментальная теорема Макса Нётера) — теорема алгебраической геометрии. (ru) En mathématiques, le théorème AF+BG est un résultat de géométrie algébrique établi par Max Noether, qui décrit sous quelles conditions l'équation d'une courbe algébrique du plan projectif complexe peut s'écrire en termes des équations de deux autres courbes algébriques. (fr)
dcterms:subject	Theorems in algebraic geometry Theorems in complex geometry
Wikipage page ID	17722329 (xsd:integer)
Wikipage revision ID	1094425029 (xsd:integer)
Link from a Wikipage to another Wikipage	Max Noether Greatest common divisor dbr:Complex_projective_plane Ideal (ring theory) Bézout's identity Local ring Algebraic curve Algebraic geometry Hilbert's Nullstellensatz Theorems in algebraic geometry Theorems in complex geometry Homogeneous polynomial Picard group Polynomial greatest common divisor Projective curve
Link from a Wikipage to an external page	http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf%7Cfirst=William%7Clast=Fulton%7Ctitle=Algebraic
sameAs	AF+BG theorem AF+BG theorem AF+BG theorem AF+BG theorem AF+BG theorem AF+BG theorem AF+BG theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:MathWorld dbt:More_footnotes dbt:Short_description dbt:Algebraic_curves_navbox
title	Noether's Fundamental Theorem (en)
urlname	NoethersFundamentalTheorem (en)
mode	cs2 (en)
has abstract	In algebraic geometry the AF+BG theorem (also known as Max Noether's fundamental theorem) is a result of Max Noether that asserts that, if the equation of an algebraic curve in the complex projective plane belongs locally (at each intersection point) to the ideal generated by the equations of two other algebraic curves, then it belongs globally to this ideal. (en) En mathématiques, le théorème AF+BG est un résultat de géométrie algébrique établi par Max Noether, qui décrit sous quelles conditions l'équation d'une courbe algébrique du plan projectif complexe peut s'écrire en termes des équations de deux autres courbes algébriques. Ce théorème est un analogue, pour les polynômes homogènes, de l'identité de Bézout, laquelle assure qu'un entier relatif h s'écrit comme somme de multiples de deux autres entiers f et g si et seulement si h est un multiple du PGCD de f et g. La condition AF+BG exprime, en termes de diviseurs (ensembles de points, avec multiplicités), une condition similaire sous laquelle un polynôme homogène H peut s'écrire comme somme de deux multiples polynomiaux de deux autres polynômes homogènes F et G. (fr) Теорема AF + BG (известная также как фундаментальная теорема Макса Нётера) — теорема алгебраической геометрии. (ru)
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prov:wasDerivedFrom	wikipedia-en:AF+BG_theorem?oldid=1094425029&ns=0
page length (characters) of wiki page	3643 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:AF+BG_theorem
is Link from a Wikipage to another Wikipage of	Max Noether Focus (geometry) Max Noether's theorem List of theorems
is foaf:primaryTopic of	wikipedia-en:AF+BG_theorem

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