Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
À l'intérieur du livre
Résultats 1-3 sur 67
Page 31
An Introduction to Algebraic Geometry William Fulton, Richard Weiss. 10. Field Extensions Suppose K is a subfield of a field L , and suppose L = K ( v ) for some νει . Let : K [ X ] be the homomorphism taking X to V. Let Ker ( ) ( F ) ...
An Introduction to Algebraic Geometry William Fulton, Richard Weiss. 10. Field Extensions Suppose K is a subfield of a field L , and suppose L = K ( v ) for some νει . Let : K [ X ] be the homomorphism taking X to V. Let Ker ( ) ( F ) ...
Page 32
... Suppose L ' is a field extension of K , y ɛ L ' such that F ( y ) = 0 . to L ' which takes X L with K ( y ) . ( c ) With L ' , y Show that the homomorphism from K [ X ] F to y induces an isomorphism of as in ( b ) , suppose Gε K [ X ] ...
... Suppose L ' is a field extension of K , y ɛ L ' such that F ( y ) = 0 . to L ' which takes X L with K ( y ) . ( c ) With L ' , y Show that the homomorphism from K [ X ] F to y induces an isomorphism of as in ( b ) , suppose Gε K [ X ] ...
Page 48
... Suppose RC SK , M and S is also a DVR . Suppose the maximal ideal of S contains M. Show that S = R. 2-27 . Show that the DVR's of Problem 2-24 are the only DVR's with quotient field k ( X ) which contain k . Show that those of 2-25 are ...
... Suppose RC SK , M and S is also a DVR . Suppose the maximal ideal of S contains M. Show that S = R. 2-27 . Show that the DVR's of Problem 2-24 are the only DVR's with quotient field k ( X ) which contain k . Show that those of 2-25 are ...
Table des matières
Chapter One Affine Algebraic Sets 1 Algebraic Preliminaries | 1 |
Affine Space and Algebraic Sets | 7 |
The Ideal of a Set of Points | 10 |
Droits d'auteur | |
26 autres sections non affichées
Autres éditions - Tout afficher
Expressions et termes fréquents
affine variety algebraic set algebraic subset algebraically closed assume Bezout's Theorem birational birationally equivalent called change of coordinates Chapter closed subvariety comaximal COROLLARY curve F curve of degree defined deg(D deg(F denote div(G div(z divisor element F and G f ɛ finite number follows form of degree function field Hint homogeneous hyperplane hypersurface induced integer intersection number isomorphism k[X₁ LEMMA Let F linear local ring maximal ideal module-finite morphism mp(F Noether's non-singular non-zero Nullstellensatz Op(C Op(V open subvariety ordinary multiple points plane curve point on F polynomial map Problem projective change projective curve projective plane curve projective variety Proof Prop PROPOSITION quadratic transformation quotient field R-module rational function residue ring homomorphism simple point subring subvariety Suppose tangent line uniformizing parameter unique V₁ vector space Xn+1 zero Ρε