| Integral Closure of Ideals, Rings, and Modules Contributor(s): Huneke, Craig (Author), Swanson, Irena (Author) |
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ISBN: 0521688604 ISBN-13: 9780521688604 Publisher: Cambridge University Press OUR PRICE: $106.40 Product Type: Paperback - Other Formats Published: October 2006 Annotation: Integral closure has played a role in number theory and algebraic geometry since the nineteenth century, but a modern formulation of the concept for ideals perhaps began with the work of Krull and Zariski in the 1930s. It has developed into a tool for the analysis of many algebraic and geometric problems. This book collects together the central notions of integral closure and presents a unified treatment. Techniques and topics covered include: behavior of the Noetherian property under integral closure, analytically unramified rings, the conductor, field separability, valuations, Rees algebras, Rees valuations, reductions, multiplicity, mixed multiplicity, joint reductions, the Brian??on-Skoda theorem, Zariski's theory of integrally closed ideals in two-dimensional regular local rings, computational aspects, adjoints of ideals and normal homomorphisms. With many worked examples and exercises, this book will provide graduate students and researchers in commutative algebra or ring theory with an approachable introduction leading into the current literature. |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - General |
| Dewey: 512.44 |
| LCCN: 2007295090 |
| Series: London Mathematical Society Lecture Notes |
| Physical Information: 0.97" H x 6.36" W x 8.94" (1.34 lbs) 448 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Integral closure has played a role in number theory and algebraic geometry since the nineteenth century, but a modern formulation of the concept for ideals perhaps began with the work of Krull and Zariski in the 1930s. It has developed into a tool for the analysis of many algebraic and geometric problems. This book collects together the central notions of integral closure and presents a unified treatment. Techniques and topics covered include: behavior of the Noetherian property under integral closure, analytically unramified rings, the conductor, field separability, valuations, Rees algebras, Rees valuations, reductions, multiplicity, mixed multiplicity, joint reductions, the Brian on-Skoda theorem, Zariski's theory of integrally closed ideals in two-dimensional regular local rings, computational aspects, adjoints of ideals and normal homomorphisms. With many worked examples and exercises, this book will provide graduate students and researchers in commutative algebra or ring theory with an approachable introduction leading into the current literature. |
Contributor Bio(s): Huneke, Craig: - Craig Huneke is the Henry J. Bischoff Professor in the Department of Mathematics, University of Kansas. |
