Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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... elements . if every non - zero element in R If R is a UFD with quotient field K , then any irreducible element Fε R [ X ] remains irreducible when considered in K [ X ] ; it follows that if F and G are polynomials in R [ X ] with no ...
... elements . if every non - zero element in R If R is a UFD with quotient field K , then any irreducible element Fε R [ X ] remains irreducible when considered in K [ X ] ; it follows that if F and G are polynomials in R [ X ] with no ...
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... element . A domain in which every ideal is principal is called a principal ideal domain , written PID . The ring of integers and the ring of polynomials in one variable over a field are examples of PID's . Every PID is a UFD . A ...
... element . A domain in which every ideal is principal is called a principal ideal domain , written PID . The ring of integers and the ring of polynomials in one variable over a field are examples of PID's . Every PID is a UFD . A ...
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... element of L which is algebraic over k is already in k . ( b ) An algebraically closed field has no module- finite field extensions except itself . 1-49 * . Let K be a field , L = K ( X ) the field of rational functions in one variable ...
... element of L which is algebraic over k is already in k . ( b ) An algebraically closed field has no module- finite field extensions except itself . 1-49 * . Let K be a field , L = K ( X ) the field of rational functions in one variable ...
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