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Author: Craig Huneke
Publisher: Cambridge University Press
Published: 2006-10-12
Total Pages: 446
ISBN-13: 0521688604
DOWNLOAD EBOOKIdeal 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 EBOOKThis 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: N. Bourbaki
Publisher: Springer Science & Business Media
Published: 1998-08-03
Total Pages: 654
ISBN-13: 3540642390
DOWNLOAD EBOOKThis is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.
Author: Jesse Elliott
Publisher: Springer Nature
Published: 2019-11-30
Total Pages: 490
ISBN-13: 3030244016
DOWNLOAD EBOOKThis 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: Brian Osserman
Publisher: American Mathematical Society
Published: 2021-12-06
Total Pages: 259
ISBN-13: 1470466651
DOWNLOAD EBOOKAuthor: Daniel Bump
Publisher: World Scientific
Published: 1998
Total Pages: 232
ISBN-13: 9789810235611
DOWNLOAD EBOOKThis 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: Craig Huneke
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 152
ISBN-13: 082180412X
DOWNLOAD EBOOKThis 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: Ruth Ingrid Michler
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 254
ISBN-13: 0821832093
DOWNLOAD EBOOKThis book presents the proceedings of two conferences, Resolution des singularites et geometrie non commutative and the Annapolis algebraic geometry conference. Research articles in the volume cover various topics of algebraic geometry, including the theory of Jacobians, singularities, applications to cryptography, and more. The book is suitable for graduate students and research mathematicians interested in algebraic geometry.
Author: Svetlana Cojocaru
Publisher: IOS Press
Published: 2005
Total Pages: 336
ISBN-13: 1586035053
DOWNLOAD EBOOKAuthor: Janusz
Publisher: American Mathematical Soc.
Published: 1995-12-05
Total Pages: 292
ISBN-13: 9780821872437
DOWNLOAD EBOOKThe 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.
