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Author: Wolmer V. Vasconcelos
Publisher: Cambridge University Press
Published: 1994-02-25
Total Pages: 343
ISBN-13: 0521454840
DOWNLOAD EBOOKThis book discusses recent developments in an important area of computational commutative algebra.
Author: David Eisenbud
Publisher: Springer Science & Business Media
Published: 2013-12-01
Total Pages: 784
ISBN-13: 1461253500
DOWNLOAD EBOOKThis 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: Gert-Martin Greuel
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 601
ISBN-13: 3662049635
DOWNLOAD EBOOKThis 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: Aron Simis
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2020-03-09
Total Pages: 356
ISBN-13: 311061698X
DOWNLOAD EBOOKThis unique book on commutative algebra is divided into two parts in order to facilitate its use in several types of courses. The first introductory part covers the basic theory, connections with algebraic geometry, computational aspects, and extensions to module theory. The more advanced second part covers material such as associated primes and primary decomposition, local rings, M-sequences and Cohen-Macaulay modules, and homological methods.
Author: Rafael Villarreal
Publisher: CRC Press
Published: 2018-10-08
Total Pages: 704
ISBN-13: 148223470X
DOWNLOAD EBOOKMonomial Algebras, Second Edition presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley–Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras. It emphasizes square-free monomials and the corresponding graphs, clutters, or hypergraphs. New to the Second Edition Four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs Two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs Full revisions of existing chapters to provide an up-to-date account of the subject Bringing together several areas of pure and applied mathematics, this book shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs. It directly links the algebraic properties of monomial algebras to combinatorial structures (such as simplicial complexes, posets, digraphs, graphs, and clutters) and linear optimization problems.
Author: Alberto Corso
Publisher: CRC Press
Published: 2005-08-15
Total Pages: 289
ISBN-13: 1420028324
DOWNLOAD EBOOKPacked 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 pres
Author: Dan Segal
Publisher: Cambridge University Press
Published: 2009-07-16
Total Pages: 134
ISBN-13: 052174766X
DOWNLOAD EBOOKExplores fundamental questions about the behaviour of word-values in groups.
Author: André Joyal
Publisher: Cambridge University Press
Published: 1995-09-14
Total Pages: 136
ISBN-13: 9780521558303
DOWNLOAD EBOOKThis book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
Author: Albrecht Pfister
Publisher: Cambridge University Press
Published: 1995-09-28
Total Pages: 191
ISBN-13: 0521467551
DOWNLOAD EBOOKA gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Author: R.K. Lazarsfeld
Publisher: Springer
Published: 2017-07-25
Total Pages: 395
ISBN-13: 3642188087
DOWNLOAD EBOOKThis two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.
