Algebraic Curves: An Introduction to Algebraic GeometryBenjamin, 1969 - 226 pages |
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... module . ( 4 ) If : R define r's for r ɛ R , rs ( r ) s . This makes = S is ... finite , { s 1 ' is denoted by Σ Rs¡ • M the submodule generated by S is ... finite - dimensional vector space if R is a field . There are Let R be a subring ...
... module . ( 4 ) If : R define r's for r ɛ R , rs ( r ) s . This makes = S is ... finite , { s 1 ' is denoted by Σ Rs¡ • M the submodule generated by S is ... finite - dimensional vector space if R is a field . There are Let R be a subring ...
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... module - finite over R. ) * 1-47ˆ . Suppose S is ring - finite over R. is module - finite over R if and only if S over R. Show that S is integral 1-48 * . Let L be a field , k an algebraically closed subfield of L. ( a ) Show that any ...
... module - finite over R. ) * 1-47ˆ . Suppose S is ring - finite over R. is module - finite over R if and only if S over R. Show that S is integral 1-48 * . Let L be a field , k an algebraically closed subfield of L. ( a ) Show that any ...
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... finite ( or module - finite ) over K ( Problem 1-44 ) . = L Case 2. F 0. We may assume F is monic . ( F ) is prime , SO F is irreducible and ( F ) therefore K [ v ] is a field , SO V is algebraic over K , finite over K. is maximal ...
... finite ( or module - finite ) over K ( Problem 1-44 ) . = L Case 2. F 0. We may assume F is monic . ( F ) is prime , SO F is irreducible and ( F ) therefore K [ v ] is a field , SO V is algebraic over K , finite over K. is maximal ...
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