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Author : Svetlana Cojocaru,Gerhard Pfister,Victor Ufnarovski
Publisher : IOS Press
Page : 336 pages
File Size : 54,5 Mb
Release : 2005
Category : Electronic books
ISBN : 9781586035051
Author : David Eisenbud,Srikanth B. Iyengar,Anurag K. Singh,J. Toby Stafford,Michel Van den Bergh
Publisher : Cambridge University Press
Page : 463 pages
File Size : 52,5 Mb
Release : 2015-11-19
Category : Mathematics
ISBN : 9781107065628
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 : Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss
Publisher : Cambridge University Press
Page : 367 pages
File Size : 43,9 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9781107129542
This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.
Author : Martin Kreuzer,Lorenzo Robbiano
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 46,7 Mb
Release : 2008-07-15
Category : Mathematics
ISBN : 9783540677338
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 : F.M.J. van Oystaeyen,A.H.M.J. Verschoren
Publisher : Springer
Page : 408 pages
File Size : 49,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540386018
Author : Wolmer Vasconcelos
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 54,5 Mb
Release : 2004-05-18
Category : Mathematics
ISBN : 3540213112
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 : David Eisenbud,Srikanth B. Iyengar,Anurag K. Singh,Michel Van den Bergh,J. Toby Stafford
Publisher : Cambridge University Press
Page : 303 pages
File Size : 47,5 Mb
Release : 2015-11-19
Category : Mathematics
ISBN : 9781107149724
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 2 focuses on the most recent research.
Author : Y. Manin
Publisher : Princeton University Press
Page : 173 pages
File Size : 44,7 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400862511
There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces." Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and quantum groups. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Igor V. Nikolaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 403 pages
File Size : 50,9 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783110543483
This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field. Contents Part I: Basics Model examples Categories and functors C∗-algebras Part II: Noncommutative invariants Topology Algebraic geometry Number theory Part III: Brief survey of NCG Finite geometries Continuous geometries Connes geometries Index theory Jones polynomials Quantum groups Noncommutative algebraic geometry Trends in noncommutative geometry
Author : Martin Kreuzer,Lorenzo Robbiano
Publisher : Springer
Page : 322 pages
File Size : 46,9 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 : Gert-Martin Greuel,Gerhard Pfister
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662049631
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.
Author : Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG
Publisher : Springer
Page : 258 pages
File Size : 54,7 Mb
Release : 2018-08-02
Category : Mathematics
ISBN : 9783319755656
This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties.
Author : Ruth Ingrid Michler
Publisher : American Mathematical Soc.
Page : 254 pages
File Size : 49,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821832097
This 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 : Giuseppe Dito
Publisher : American Mathematical Soc.
Page : 143 pages
File Size : 40,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821841471
This volume represents the proceedings of the conference on Topics in Deformation Quantization and Non-Commutative Structures held in Mexico City in September 2005. It contains survey papers and original contributions by various experts in the fields of deformation quantization and non-commutative derived algebraic geometry in the interface between mathematics and physics. It also contains an article based on the XI Memorial Lectures given by M. Kontsevich, which were delivered as part of the conference. This is an excellent introductory volume for readers interested in learning about quantization as deformation, Hopf algebras, and Hodge structures in the framework of non-commutative algebraic geometry.
Author : Anonim
Publisher : Unknown
Page : 404 pages
File Size : 54,7 Mb
Release : 1964
Category : Associative rings
ISBN : 0387111530