Homological And Computational Methods In Commutative Algebra PDF Download
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Author | : Aldo Conca |
Publisher | : Springer |
Total Pages | : 265 |
Release | : 2017-11-16 |
Genre | : Mathematics |
ISBN | : 3319619438 |
Download Homological and Computational Methods in Commutative Algebra Book in PDF, ePub and Kindle
This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.
Author | : Wolmer Vasconcelos |
Publisher | : Springer Science & Business Media |
Total Pages | : 432 |
Release | : 2004-05-18 |
Genre | : Mathematics |
ISBN | : 9783540213116 |
Download Computational Methods in Commutative Algebra and Algebraic Geometry Book in PDF, ePub and Kindle
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 | : Wolmer Vasconcelos |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2004-06-01 |
Genre | : Mathematics |
ISBN | : 9783642589515 |
Download Computational Methods in Commutative Algebra and Algebraic Geometry Book in PDF, ePub and Kindle
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 | : Andrea Ferretti |
Publisher | : American Mathematical Society |
Total Pages | : 394 |
Release | : 2023-09-26 |
Genre | : Mathematics |
ISBN | : 1470471272 |
Download Commutative Algebra Book in PDF, ePub and Kindle
This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra. The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra. Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.
Author | : David Eisenbud |
Publisher | : Springer |
Total Pages | : 346 |
Release | : 1999-07 |
Genre | : Mathematics |
ISBN | : |
Download Commutative Algebra, Algebraic Geometry, and Computational Methods Book in PDF, ePub and Kindle
This volume contains papers presented at the International Conference on Commutative Algebra, Algebraic geometry, and Computational methods held in Hanoi in 1996, as well as papers written subsequently. It features both expository articles as well as research papers on a range of currently active areas in commutative algebra, algebraic geometry (particularly surveys on intersection theory) and combinatorics. In addition, a special feature is a section on the life and work of Wolfgang Vogel, who was an organiser of the conference.
Author | : Andrea Ferretti |
Publisher | : American Mathematical Society |
Total Pages | : 432 |
Release | : 2023-11-30 |
Genre | : Mathematics |
ISBN | : 1470471280 |
Download Homological Methods in Commutative Algebra Book in PDF, ePub and Kindle
This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author's book, Commutative Algebra. The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, starting from categorical language up to the construction of derived functors and spectral sequences. A full proof of the celebrated Freyd-Mitchell theorem on the embeddings of small Abelian categories is included. The second part of the book is devoted to the application of these techniques in commutative algebra through the study of projective, injective, and flat modules, the construction of explicit resolutions via the Koszul complex, and the properties of regular sequences. The theory is then used to understand the properties of regular rings, Cohen-Macaulay rings and modules, Gorenstein rings and complete intersections. Overall, this book is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra. The clear and thorough presentation of the material, along with the many examples and exercises of varying difficulty, make it an excellent choice for self-study or as a reference for researchers.
Author | : Alberto Corso |
Publisher | : CRC Press |
Total Pages | : |
Release | : 2017-08-09 |
Genre | : |
ISBN | : 9781138402126 |
Download Commutative Algebra Book in PDF, ePub and Kindle
Packed with contributions from international experts, Commutative Algebra: Geometric, Homological, Combinatorial, and Computational Aspects features new research results that borrow methods from neighboring fields such as combinatorics, homological algebra, polyhedral geometry, symbolic computation, and topology. This book consists of articles presented during two conferences held in Spain and Portugal in June, 2003. It encompasses a variety of topics, including blowup algebras, Castelnuovo-Mumford regularity, integral closure and normality, Koszul homology, liaison theory, multiplicities, polarization, and reductions of ideals. This comprehensive volume will stimulate further research in the field.
Author | : Thomas Becker |
Publisher | : Springer Science & Business Media |
Total Pages | : 587 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461209137 |
Download Gröbner Bases Book in PDF, ePub and Kindle
The origins of the mathematics in this book date back more than two thou sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.
Author | : Gert-Martin Greuel |
Publisher | : Springer Science & Business Media |
Total Pages | : 601 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3662049635 |
Download A Singular Introduction to Commutative Algebra Book in PDF, ePub and Kindle
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 | : S. Raghavan |
Publisher | : |
Total Pages | : 152 |
Release | : 1975 |
Genre | : Algebra, Homological |
ISBN | : |
Download Homological Methods in Commutative Algebra Book in PDF, ePub and Kindle