Author : David Eisenbud
Publisher : Cambridge University Press
Page : 463 pages
File Size : 24,67 MB
Release : 2015-11-19
Category : Mathematics
ISBN : 1107065623
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.
Author : Wolmer Vasconcelos
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 27,62 MB
Release : 2004-05-18
Category : Mathematics
ISBN : 9783540213116
This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.
Author : Gwyn Bellamy
Publisher : Cambridge University Press
Page : 367 pages
File Size : 43,61 MB
Release : 2016-06-20
Category : Mathematics
ISBN : 1107129540
This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.
Author : Alain Connes
Publisher : Springer
Page : 364 pages
File Size : 24,63 MB
Release : 2003-12-15
Category : Mathematics
ISBN : 3540397027
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Author : Martin Kreuzer
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 13,65 MB
Release : 2008-07-15
Category : Mathematics
ISBN : 354067733X
This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.
Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 23,97 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461253500
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 : Svetlana Cojocaru
Publisher : IOS Press
Page : 336 pages
File Size : 35,94 MB
Release : 2005
Category : Electronic books
ISBN : 1586035053
Author : Marco Fontana
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 45,67 MB
Release : 2010-09-29
Category : Mathematics
ISBN : 144196990X
Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.
Author : Thomas A. Garrity
Publisher : American Mathematical Soc.
Page : 363 pages
File Size : 35,78 MB
Release : 2013-02-01
Category : Mathematics
ISBN : 0821893963
Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex
Author : Gert-Martin Greuel
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 33,41 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3662049635
This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.
