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- catalog abstract ""This book presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. Elimination theory is a classical topic in commutative algebra and algebraic geometry, and has become of renewed importance in the context of applied and computational algebra. This book provides a valuable complement to sparse elimination theory in that it presents, in careful detail, the algebraic difficulties of working over general base rings, which is essential for many applications including arithmetic geometry. Necessary tools concerning monoids of weights, generic polynomials, and regular sequences are treated independently in the first part of the book. Supplements following each section provide extra details and insightful examples."--Jacket.".
- catalog contributor b12161547.
- catalog contributor b12161548.
- catalog created "c2001.".
- catalog date "2001".
- catalog date "c2001.".
- catalog dateCopyrighted "c2001.".
- catalog description ""This book presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. Elimination theory is a classical topic in commutative algebra and algebraic geometry, and has become of renewed importance in the context of applied and computational algebra. This book provides a valuable complement to sparse elimination theory in that it presents, in careful detail, the algebraic difficulties of working over general base rings, which is essential for many applications including arithmetic geometry. Necessary tools concerning monoids of weights, generic polynomials, and regular sequences are treated independently in the first part of the book. Supplements following each section provide extra details and insightful examples."--Jacket.".
- catalog description "1 Kronecker Extensions 1 -- 2 Modules and Kronecker Extensions 6 -- 3 Numerical Monoids 13 -- 4 Relations of Numerical Monoids 23 -- 5 Splitting of Numerical Monoids 36 -- II Regular Sequences -- 6 Regular Sequences and Complete Intersections 41 -- 7 Graded Complete Intersections 53 -- 8 Generic Regular Sequences 60 -- 9 Generic Structure of the Principal Component 75 -- III Elimination -- 10 Basics of Elimination 81 -- 11 Main Case for Generic Regular Sequences 85 -- 12 Main Case for Regular Sequences 96 -- IV Resultants -- 13 Resultant Ideals 105 -- 14 Resultant Divisors and Duality 109 -- 15 Resultants 119 -- 16 Formulas on Resultants 129.".
- catalog description "Includes bibliographical references (p. 137-139) and index.".
- catalog extent "vii, 142 p. ;".
- catalog identifier "1568811519".
- catalog isPartOf "Research notes in mathematics (Boston, Mass.) ; 8.".
- catalog isPartOf "Research notes in mathematics ; v. 8".
- catalog issued "2001".
- catalog issued "c2001.".
- catalog language "eng".
- catalog publisher "Natick, Mass. : A K Peters,".
- catalog subject "512.9/434 21".
- catalog subject "Elimination.".
- catalog subject "Intersection theory.".
- catalog subject "Projective spaces.".
- catalog subject "QA192 .S32 2001".
- catalog subject "Sequences (Mathematics)".
- catalog tableOfContents "1 Kronecker Extensions 1 -- 2 Modules and Kronecker Extensions 6 -- 3 Numerical Monoids 13 -- 4 Relations of Numerical Monoids 23 -- 5 Splitting of Numerical Monoids 36 -- II Regular Sequences -- 6 Regular Sequences and Complete Intersections 41 -- 7 Graded Complete Intersections 53 -- 8 Generic Regular Sequences 60 -- 9 Generic Structure of the Principal Component 75 -- III Elimination -- 10 Basics of Elimination 81 -- 11 Main Case for Generic Regular Sequences 85 -- 12 Main Case for Regular Sequences 96 -- IV Resultants -- 13 Resultant Ideals 105 -- 14 Resultant Divisors and Duality 109 -- 15 Resultants 119 -- 16 Formulas on Resultants 129.".
- catalog title "Regular sequences and resultants / Günter Scheja, Uwe Storch.".
- catalog type "text".