Download or read book Integral Closure of Ideals Rings and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Download or read book Integral Closure written by Wolmer Vasconcelos and published by Springer Science & Business Media. This book was released on 2005-11-04 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Rings Modules and Closure Operations written by Jesse Elliott and published by Springer Nature. This book was released on 2019-11-30 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tight Closure and Its Applications written by Craig Huneke and published by American Mathematical Soc.. This book was released on 1996 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Commutative Ring Theory written by Hideyuki Matsumura and published by Cambridge University Press. This book was released on 1989-05-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Download or read book Commutative Algebra written by David Eisenbud and published by Springer Science & Business Media. This book was released on 1995-03-30 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Geometry written by Daniel Bump and published by World Scientific. This book was released on 1998 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Number Fields written by Janusz and published by American Mathematical Soc.. This book was released on 1995-12-05 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Concise Introduction to Algebraic Varieties written by Brian Osserman and published by American Mathematical Society. This book was released on 2021-12-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Divisor Class Group of a Krull Domain written by Robert M. Fossum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Commutative Algebra written by Marco Fontana and published by Springer. This book was released on 2014-07-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Commutative Ring Theory written by Cahen and published by CRC Press. This book was released on 1993-10-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: " Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers the spectra of rings chain conditions, dimension theory, and Jaffard rings fiber products group rings, semigroup rings, and graded rings class groups linear groups integer-valued polynomials rings of finite fractions big Cohen-Macaulay modules and much more!"
Download or read book Ideal Systems written by Franz Halter-Koch and published by CRC Press. This book was released on 1998-04-21 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Provides for the first time a concise introduction to general and multiplicative ideal theory, valid for commutative rings and monoids and presented in the language of ideal systems on (commutative) monoids."
Download or read book Field Arithmetic written by Michael D. Fried and published by Springer Science & Business Media. This book was released on 2008-04-09 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005.
Download or read book Fundamentals of Advanced Mathematics 1 written by Henri Bourles and published by Elsevier. This book was released on 2017-07-10 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations). The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients. Part of the New Mathematical Methods, Systems, and Applications series Presents the notions, results, and proofs necessary to understand and master the various topics Provides a unified notation, making the task easier for the reader. Includes several summaries of mathematics for engineers
Download or read book Commutative Algebra Volume I written by Oscar Zariski and published by Courier Dover Publications. This book was released on 2019-11-13 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: A precise, fundamental study of commutative algebra, this largely self-contained treatment is the first in a two-volume set. Intended for advanced undergraduates and graduate students in mathematics, its prerequisites are the rudiments of set theory and linear algebra, including matrices and determinants. The opening chapter develops introductory notions concerning groups, rings, fields, polynomial rings, and vector spaces. Subsequent chapters feature an exposition of field theory and classical material concerning ideals and modules in arbitrary commutative rings, including detailed studies of direct sum decompositions. The final two chapters explore Noetherian rings and Dedekind domains. This work prepares readers for the more advanced topics of Volume II, which include valuation theory, polynomial and power series rings, and local algebra.
Download or read book Non Commutative Valuation Rings and Semi Hereditary Orders written by Hidetoshi Marubayashi and published by Springer Science & Business Media. This book was released on 1997-05-31 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much progress has been made during the last decade on the subjects of non commutative valuation rings, and of semi-hereditary and Priifer orders in a simple Artinian ring which are considered, in a sense, as global theories of non-commu tative valuation rings. So it is worth to present a survey of the subjects in a self-contained way, which is the purpose of this book. Historically non-commutative valuation rings of division rings were first treat ed systematically in Schilling's Book [Sc], which are nowadays called invariant valuation rings, though invariant valuation rings can be traced back to Hasse's work in [Has]. Since then, various attempts have been made to study the ideal theory of orders in finite dimensional algebras over fields and to describe the Brauer groups of fields by usage of "valuations", "places", "preplaces", "value functions" and "pseudoplaces". In 1984, N. 1. Dubrovin defined non-commutative valuation rings of simple Artinian rings with notion of places in the category of simple Artinian rings and obtained significant results on non-commutative valuation rings (named Dubrovin valuation rings after him) which signify that these rings may be the correct def inition of valuation rings of simple Artinian rings. Dubrovin valuation rings of central simple algebras over fields are, however, not necessarily to be integral over their centers.
