Regular Sequences and Resultants

This carefully prepared manuscript 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 it has become of renewed importance recently in the context of applied and computational algebra. This monograph provides a valuable complement to sparse elimination theory in that it presents in careful detail the algebraic difficulties from working over general base rings. This is essential for applications in arithmetic geometry and many other places. Necessary tools concerning monoids of weights, generic polynomials and regular sequences are treated independently in the first part of the book. Many supplements added to each chapter provide extra details and insightful examples. Necessary tools concerning monoids of weights, generic polynomials and regular sequences are treated independently in the first part of the book. Many supplements added to each chapter provide extra details and insightful examples.

This carefully prepared manuscript 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 it has become of renewed importance recently in the context of applied and computational algebra. This monograph provides a valuable complement to sparse elimination theory in that it presents in careful detail the algebraic difficulties from working over general base rings. This is essential for applications in arithmetic geometry and many other places. Necessary tools concerning monoids of weights, generic polynomials and regular sequences are treated independently in the first part of the book. Many supplements added to each chapter provide extra details and insightful examples. Necessary tools concerning monoids of weights, generic polynomials and regular sequences are treated independently in the first part of the book. Many supplements added to each chapter provide extra details and insightful examples.

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This research monograph presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. It describes the algebraic difficulties of working over general base rings, which is essential for many applications including arithmetic geometry. In particular, a new approach to the construction and interpretation of resultants and their divisors has been developed using explicit duality for complete intersections. Necessary tools concerning monoids of weights, generic polynomials, and regular sequences are treated independently. Supplements to each section provide extra details and examples. Scheja teaches at Universit<:a>t T<:u>bingen. Storch teaches at Ruhr-Universit<:a>t Bochum. Annotation c. Book News, Inc., Portland, OR (booknews.com)