Undergraduate Commutative Algebra

Author: Miles Reid
Publisher: Cambridge University Press
ISBN: 9780521458894
Format: PDF, Kindle
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In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins with a discussion of modules and Noetherian rings before moving on to finite extensions and the Noether normalization. Sections on the nullstellensatz and rings of fractions precede sections on primary decomposition and normal integral domains. This book is ideal for anyone seeking a primer on commutative algebra.

Steps in Commutative Algebra

Author: R. Y. Sharp
Publisher: Cambridge University Press
ISBN: 9780521646239
Format: PDF, ePub, Docs
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This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen–Macaulay rings, have been added. This book is ideal as a route into commutative algebra.

Undergraduate Algebraic Geometry

Author: Miles Reid
Publisher: Cambridge University Press
ISBN: 9780521356626
Format: PDF, ePub, Mobi
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This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.

Introductory Lectures on Rings and Modules

Author: John A. Beachy
Publisher: Cambridge University Press
ISBN: 9780521644075
Format: PDF, Kindle
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A first-year graduate text or reference for advanced undergraduates on noncommutative aspects of rings and modules.

Computational Algebraic Geometry

Author: Hal Schenck
Publisher: Cambridge University Press
ISBN: 9780521536509
Format: PDF, ePub, Docs
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This 2003 book investigates interplay between algebra and geometry. Covers: homological algebra, algebraic combinatorics and algebraic topology, and algebraic geometry.

Young Tableaux

Author: William Fulton
Publisher: Cambridge University Press
ISBN: 9780521567244
Format: PDF, Docs
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Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.

Fourier Analysis on Finite Groups and Applications

Author: Audrey Terras
Publisher: Cambridge University Press
ISBN: 9780521457187
Format: PDF, Mobi
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A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.

Riemann Surfaces and Algebraic Curves

Author: Renzo Cavalieri
Publisher: Cambridge University Press
ISBN: 1316798933
Format: PDF, ePub, Docs
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Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

Elements of the Representation Theory of Associative Algebras Volume 1

Author: Ibrahim Assem
Publisher: Cambridge University Press
ISBN: 1139443186
Format: PDF, ePub, Docs
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This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields.