Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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Page 3
... field k . The quotient field of k [ X , ... , X ] is written k ( X , ... , X ) , and is called the field of rational functions in n variables over k . n n 4 If 4 : R S is a ring homomorphism , the set 1 ( 0 ) of elements mapped to zero ...
... field k . The quotient field of k [ X , ... , X ] is written k ( X , ... , X ) , and is called the field of rational functions in n variables over k . n n 4 If 4 : R S is a ring homomorphism , the set 1 ( 0 ) of elements mapped to zero ...
Page 47
... quotient field of R. Then ( when t is fixed ) any non - zero element Ζε κ has a unique expression z = ut ut " , u a ... quotient field Q. is a 2-26 * . Let R be a DVR with quotient AFFINE VARIETIES 47.
... quotient field of R. Then ( when t is fixed ) any non - zero element Ζε κ has a unique expression z = ut ut " , u a ... quotient field Q. is a 2-26 * . Let R be a DVR with quotient AFFINE VARIETIES 47.
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... quotient field k ( X ) which contain k . Show that those of 2-25 are the only DVR's with quotient field Q. 2-28 . An order function on a field K is a function satisfying : ф from K onto ZU { } , ( i ) ( a ) = ∞ if and only if a = 0 ...
... quotient field k ( X ) which contain k . Show that those of 2-25 are the only DVR's with quotient field Q. 2-28 . An order function on a field K is a function satisfying : ф from K onto ZU { } , ( i ) ( a ) = ∞ if and only if a = 0 ...
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 | |
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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