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Author: Craig Huneke
Publisher: Cambridge University Press
Published: 2006-10-12
Total Pages: 446
ISBN-13: 0521688604
DOWNLOAD EBOOK →Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Author: Wolmer Vasconcelos
Publisher: Springer Science & Business Media
Published: 2005-11-04
Total Pages: 528
ISBN-13: 3540265031
DOWNLOAD EBOOK →This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. It gives a comprehensive treatment of Rees algebras and multiplicity theory while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.
Author: Jesse Elliott
Publisher: Springer Nature
Published: 2019-11-30
Total Pages: 490
ISBN-13: 3030244016
DOWNLOAD EBOOK →This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.
Author: Craig Huneke
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 152
ISBN-13: 082180412X
DOWNLOAD EBOOK →This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.
Author: Hideyuki Matsumura
Publisher: Cambridge University Press
Published: 1989-05-25
Total Pages: 338
ISBN-13: 9780521367646
DOWNLOAD EBOOK →This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Author: David Eisenbud
Publisher: Springer Science & Business Media
Published: 1995-03-30
Total Pages: 822
ISBN-13: 9780387942698
DOWNLOAD EBOOK →This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Author: Daniel Bump
Publisher: World Scientific
Published: 1998
Total Pages: 232
ISBN-13: 9789810235611
DOWNLOAD EBOOK →This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used. A taste of the deeper theory is given: some topics, such as local algebra and ramification theory, are treated in depth. The book culminates with a selection of topics from the theory of algebraic curves, including the Riemann-Roch theorem, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.
Author: Janusz
Publisher: American Mathematical Soc.
Published: 1995-12-05
Total Pages: 292
ISBN-13: 9780821872437
DOWNLOAD EBOOK →The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such as the arithmetic of fields, Dedekind domains, and valuations. The next two chapters discuss class field theory for number fields. The concluding chapter serves as an illustration of the concepts introduced in previous chapters. In particular, some interesting calculations with quadratic fields show the use of the norm residue symbol. For the second edition the author added some new material, expanded many proofs, and corrected errors found in the first edition. The main objective, however, remains the same as it was for the first edition: to give an exposition of the introductory material and the main theorems about class fields of algebraic number fields that would require as little background preparation as possible. Janusz's book can be an excellent textbook for a year-long course in algebraic number theory; the first three chapters would be suitable for a one-semester course. It is also very suitable for independent study.
Author: Brian Osserman
Publisher: American Mathematical Society
Published: 2021-12-02
Total Pages: 259
ISBN-13: 1470460130
DOWNLOAD EBOOK →A Concise Introduction to Algebraic Varieties is designed for a one-term introductory course on algebraic varieties over an algebraically closed field, and it provides a solid basis for a course on schemes and cohomology or on specialized topics, such as toric varieties and moduli spaces of curves. The book balances generality and accessibility by presenting local and global concepts, such as nonsingularity, normality, and completeness using the language of atlases, an approach that is most commonly associated with differential topology. The book concludes with a discussion of the Riemann-Roch theorem, the Brill-Noether theorem, and applications. The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic point-set topology. A course in graduate algebra is helpful but not required. The book includes appendices presenting useful background in complex analytic topology and commutative algebra and provides plentiful examples and exercises that help build intuition and familiarity with algebraic varieties.
Author: Marco Fontana
Publisher: Springer
Published: 2014-07-15
Total Pages: 372
ISBN-13: 1493909258
DOWNLOAD EBOOK →This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.
