Steps In Commutative Algebra
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Steps In Commutative Algebra
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Author : R. Y. Sharp
language : en
Publisher: Cambridge University Press
Release Date : 2000
Steps In Commutative Algebra written by R. Y. Sharp 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 2000 with Mathematics categories.
Introductory account of commutative algebra, aimed at students with a background in basic algebra.
Steps In Commutative Algebra
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Author : Rodney Y. Sharp
language : en
Publisher: Cambridge University Press
Release Date : 1990-08-30
Steps In Commutative Algebra written by Rodney Y. Sharp 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 1990-08-30 with Mathematics categories.
This introductory account of commutative algebra, geared to students with only a basic algebraic background, will provide a foundation from which the reader can proceed to more advanced levels or to algebraic geometry.
Introduction To Commutative Algebra
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Author : Michael F. Atiyah
language : en
Publisher: CRC Press
Release Date : 2018-03-09
Introduction To Commutative Algebra written by Michael F. Atiyah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-09 with Mathematics categories.
First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
Undergraduate Commutative Algebra
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Author : Miles Reid
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-30
Undergraduate Commutative Algebra written by Miles Reid 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 1995-11-30 with Mathematics categories.
Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.
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.
Introduction To Algebraic Geometry And Commutative Algebra
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Author : Dilip P Patil
language : en
Publisher: World Scientific Publishing Company
Release Date : 2010-03-31
Introduction To Algebraic Geometry And Commutative Algebra written by Dilip P Patil and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-31 with Mathematics categories.
This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics. Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.
Mostly Commutative Algebra
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Author : Antoine Chambert-Loir
language : en
Publisher: Springer Nature
Release Date : 2021-04-08
Mostly Commutative Algebra written by Antoine Chambert-Loir and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-08 with Mathematics categories.
This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.
Commutative Algebra
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Author : William J. Heinzer
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Commutative Algebra written by William J. Heinzer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This volume contains refereed papers on themes explored at the AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, held at Mount Holyoke College in 1992. The conference featured a series of one-hour invited lectures on recent advances in commutative algebra and interactions with such areas as algebraic geometry, representation theory, and combinatorics. The major themes of the conference were tight closure Hilbert functions, birational algebra, free resolutions and the homological conjectures, Rees algebras, and local cohomology. With contributions by several leading experts in the field, this volume provides an excellent survey of current research in commutative algebra.
Computational Algebra Course And Exercises With Solutions
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Author : Ihsen Yengui
language : en
Publisher: World Scientific
Release Date : 2021-05-17
Computational Algebra Course And Exercises With Solutions written by Ihsen Yengui and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-17 with Mathematics categories.
This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.
An Introduction To Commutative Algebra
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Author : Huishi Li
language : en
Publisher: World Scientific Publishing Company
Release Date : 2004-08-10
An Introduction To Commutative Algebra written by Huishi Li and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-10 with Mathematics categories.
Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure. It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry. Many worked examples and a number of problem (with hints) can be found in the volume. It is also a convenient reference for researchers who use basic commutative algebra.