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Regular sequences and resultants

Author: Günter Scheja; Uwe Storch
Publisher: Natick, Mass. : A K Peters, ©2001.
Series: Research notes in mathematics (Boston, Mass.), 8.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"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  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Günter Scheja; Uwe Storch
ISBN: 1568811519 9781568811512
OCLC Number: 46401634
Description: viii, 142 p. ; 24 cm.
Contents: 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.
Series Title: Research notes in mathematics (Boston, Mass.), 8.
Responsibility: Günter Scheja, Uwe Storch.
More information:

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.

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