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| Author | : Craig Huneke |
| Publisher | : Cambridge University Press |
| Total Pages | : 446 |
| Release | : 2006-10-12 |
| Genre | : Mathematics |
| ISBN | : 0521688604 |
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 |
| Total Pages | : 528 |
| Release | : 2005-11-04 |
| Genre | : Mathematics |
| ISBN | : 3540265031 |
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 |
| Total Pages | : 490 |
| Release | : 2019-11-30 |
| Genre | : Mathematics |
| ISBN | : 3030244016 |
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. |
| Total Pages | : 152 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 082180412X |
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 |
| Total Pages | : 338 |
| Release | : 1989-05-25 |
| Genre | : Mathematics |
| ISBN | : 9780521367646 |
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 |
| Total Pages | : 822 |
| Release | : 1995-03-30 |
| Genre | : Mathematics |
| ISBN | : 9780387942698 |
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 |
| Total Pages | : 232 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9789810235611 |
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. |
| Total Pages | : 292 |
| Release | : 1995-12-05 |
| Genre | : Mathematics |
| ISBN | : 9780821872437 |
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 |
| Total Pages | : 259 |
| Release | : 2021-12-02 |
| Genre | : Mathematics |
| ISBN | : 1470460130 |
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 | : Robert M. Fossum |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 157 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642884059 |
There are two main purposes for the wntmg of this monograph on factorial rings and the associated theory of the divisor class group of a Krull domain. One is to collect the material which has been published on the subject since Samuel's treatises from the early 1960's. Another is to present some of Claborn's work on Dedekind domains. Since I am not an historian, I tread on thin ice when discussing these matters, but some historical comments are warranted in introducing this material. Krull's work on finite discrete principal orders originating in the early 1930's has had a great influence on ring theory in the suc ceeding decades. Mori, Nagata and others worked on the problems Krull suggested. But it seems to me that the theory becomes most useful after the notion of the divisor class group has been made func torial, and then related to other functorial concepts, for example, the Picard group. Thus, in treating the group of divisors and the divisor class group, I have tried to explain and exploit the functorial properties of these groups. Perhaps the most striking example of the exploitation of this notion is seen in the works of I. Danilov which appeared in 1968 and 1970.
