Homological Methods In Commutative Algebra
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Homological Methods In Commutative Algebra
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Author : S. Raghavan
language : en
Publisher:
Release Date : 1975
Homological Methods In Commutative Algebra written by S. Raghavan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Algebra, Homological categories.
Homological Methods In Commutative Algebra
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Author : Andrea Ferretti
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-30
Homological Methods In Commutative Algebra written by Andrea Ferretti and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-30 with Mathematics categories.
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.
Homological Methods In Commutative Algebra
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Author : Andrea Ferretti
language : en
Publisher: American Mathematical Society
Release Date : 2023-12-05
Homological Methods In Commutative Algebra written by Andrea Ferretti and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-05 with Mathematics categories.
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.
Applications Of Homological Methods In Commutative Algebra
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Author : Gunnar Sjödin
language : en
Publisher:
Release Date : 19??
Applications Of Homological Methods In Commutative Algebra written by Gunnar Sjödin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 19?? with categories.
Homological Methods In Commutative Algebra
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Author : Hiroko Tanaka
language : en
Publisher:
Release Date : 1973
Homological Methods In Commutative Algebra written by Hiroko Tanaka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
Commutative Algebra
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Commutative Algebra written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.
Homological Methods In Commutative Algebra
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Author : Raghavan Balwant S. Singh
language : en
Publisher:
Release Date : 1975
Homological Methods In Commutative Algebra written by Raghavan Balwant S. Singh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Computational Methods In Commutative Algebra And Algebraic Geometry
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Author : Wolmer Vasconcelos
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-18
Computational Methods In Commutative Algebra And Algebraic Geometry written by Wolmer Vasconcelos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-18 with Mathematics categories.
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.
Algebraic Geometry And Commutative Algebra
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Author : Siegfried Bosch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-15
Algebraic Geometry And Commutative Algebra written by Siegfried Bosch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-15 with Mathematics categories.
Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.
An Introduction To Homological Algebra
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Author : Charles A. Weibel
language : en
Publisher: Cambridge University Press
Release Date : 1995-10-27
An Introduction To Homological Algebra written by Charles A. Weibel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-27 with Mathematics categories.
The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.