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Author : R. Y. Sharp
Publisher : Cambridge University Press
Page : 371 pages
File Size : 55,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9780521646239
Introductory account of commutative algebra, aimed at students with a background in basic algebra.
Author : Michael F. Atiyah,I.G. MacDonald
Publisher : CRC Press
Page : 140 pages
File Size : 55,9 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9780429973260
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.
Author : Antoine Chambert-Loir
Publisher : Springer Nature
Page : 466 pages
File Size : 42,5 Mb
Release : 2021-04-08
Category : Mathematics
ISBN : 9783030615956
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.
Author : Steven Kleiman,Allen Altman
Publisher : Unknown
Page : 208 pages
File Size : 54,9 Mb
Release : 2013-01-01
Category : Commutative algebra
ISBN : 0988557215
There is no shortage of books on Commutative Algebra, but the present book is different. Most books are monographs, with extensive coverage. There is one notable exception: Atiyah and Macdonald’s 1969 classic. It is a clear, concise, and efficient textbook, aimed at beginners, with a good selection of topics. So it has remained popular. However, its age and flaws do show. So there is need for an updated and improved version, which the present book aims to be.
Author : Miles Reid
Publisher : Cambridge University Press
Page : 172 pages
File Size : 50,8 Mb
Release : 1995-11-30
Category : Mathematics
ISBN : 0521458897
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.
Author : Martin Kreuzer,Lorenzo Robbiano
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 46,9 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 : Gert-Martin Greuel,Gerhard Pfister
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 50,6 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 : A. Rosenberg
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 42,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401584302
This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others.
Author : Craig Huneke,Irena Swanson
Publisher : Cambridge University Press
Page : 446 pages
File Size : 55,8 Mb
Release : 2006-10-12
Category : Mathematics
ISBN : 9780521688604
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Author : Martin Kreuzer,Lorenzo Robbiano
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 47,9 Mb
Release : 2008-07-05
Category : Mathematics
ISBN : 9783540706281
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 : David Eisenbud,Srikanth B. Iyengar,Anurag K. Singh,J. Toby Stafford,Michel Van den Bergh
Publisher : Cambridge University Press
Page : 463 pages
File Size : 43,8 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 : Michael F. Atiyah,I.G. MacDonald
Publisher : CRC Press
Page : 140 pages
File Size : 42,7 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9780429973260
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.
Author : Andrea Ferretti
Publisher : American Mathematical Society
Page : 394 pages
File Size : 54,5 Mb
Release : 2023-09-26
Category : Mathematics
ISBN : 9781470471279
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 : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 139 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662042038
This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.
Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 52,9 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9780486474175
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.