Algebraic Varieties

Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Format: PDF, Kindle
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An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

Arithmetic of Blowup Algebras

Author: Wolmer V. Vasconcelos
Publisher: Cambridge University Press
ISBN: 9780521454841
Format: PDF, Docs
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This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.

Commutative Algebra

Author: R. Y. Sharp
Publisher: Cambridge University Press
ISBN: 0521271258
Format: PDF
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This book is concerned with the research conducted in the late 1970s and early 1980s in the theory of commutative Neotherian rings. It consists of articles by invited speakers at the Symposium of Commutative Algebra held at the University of Durham in July 1981; these articles are all based on lectures delivered at the Symposium. The purpose of this book is to provide a record of at least some aspects of the Symposium, which several of the world leaders in the field attended. Several articles are included which provide surveys, incorporating historical perspective, details of progress made and indications of possible future lines of investigation. The book will be of interest to scholars of commutative and local algebra.

Integral Closure of Ideals Rings and Modules

Author: Craig Huneke
Publisher: Cambridge University Press
ISBN: 0521688604
Format: PDF, ePub
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Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Commutative Algebra

Author: J. T. Knight
Publisher: Cambridge University Press
ISBN: 0521081939
Format: PDF, ePub
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This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.

Geometric and Cohomological Group Theory

Author: Peter H. Kropholler
Publisher: Cambridge University Press
ISBN: 131662322X
Format: PDF, ePub
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Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.

The Q Schur Algebra

Author: S. Donkin
Publisher: Cambridge University Press
ISBN: 9780521645584
Format: PDF, Mobi
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This book focuses on the representation theory of q-Schur algebras and connections with the representation theory of Hecke algebras and quantum general linear groups. The aim is to present, from a unified point of view, quantum analogs of certain results known already in the classical case. The approach is largely homological, based on Kempf's vanishing theorem for quantum groups and the quasi-hereditary structure of the q-Schur algebras. Beginning with an introductory chapter dealing with the relationship between the ordinary general linear groups and their quantum analogies, the text goes on to discuss the Schur Functor and the 0-Schur algebra. The next chapter considers Steinberg's tensor product and infinitesimal theory. Later sections of the book discuss tilting modules, the Ringel dual of the q-Schur algebra, Specht modules for Hecke algebras, and the global dimension of the q-Schur algebras. An appendix gives a self-contained account of the theory of quasi-hereditary algebras and their associated tilting modules. This volume will be primarily of interest to researchers in algebra and related topics in pure mathematics.

Finite Von Neumann Algebras and Masas

Author: Allan Sinclair
Publisher: Cambridge University Press
ISBN: 0521719194
Format: PDF, ePub
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A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann algebras. The theory of singular masas and Sorin Popa's methods of constructing singular and semi-regular masas in general separable II1 factor are explored. Appendices cover the ultrapower of an II1 factor and the properties of unbounded operators required for perturbation results. Proofs are given in considerable detail and standard basic examples are provided, making the book understandable to postgraduates with basic knowledge of von Neumann algebra theory.