Content: Commutative Algebra is the study of commutative rings, and their modules and ideals. This theory has developed over the last years not just as an area of algebra considered for its own sake, but as a tool in the study of two enormously important branches of mathematics: algebraic geometry and algebraic number theory. The unification which results, where the same underlying algebraic structures arise both in geometry and in number theory, has been one of the crowning glories of twentieth century mathematics and still plays an absolutely fundamental role in current work in both these fields. One simple example of this unification will be familiar already to anyone who has noticed the strong parallels between the ring Z a Euclidean Domain and hence also a Unique Factorization Domain and the ring F[X] of polynomials over a field which has both the same properties.
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Barn Showing the link between commutative ring theory and algebraic geometry, this book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Shafarevich, Basic algebraic geometry I, Springer, R. Quang Dao marked it as to-read Feb 07, This book is not yet featured on Listopia. See also my Surface links.
Trivia About Undergraduate Com The emphasis is on concrete examples of curves, surfaces, projective arieties and singularities, as illustrated in my Park City lecture notes [Chapters] and in the book in progress [More Chapters]. Chris is currently reading it Sep 21, Books by Miles Reid. Students may wish to study more material in a parallel self-help seminar I can try to arrange exam credit for this as necessary. To see what your friends thought of this book, please sign up.
Technical foundational material, for example on commutative algebra and affine schemes, on sheaves and coherent cohomology, will be introduced as required, without detailed proofs. Teena marked it as to-read Aug 06, Gautam is currently reading it Jan 20, Feb 18, Siggy rated it it was amazing Shelves: To ask other readers questions about Undergraduate Commutative Algebraplease sign up.
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Want to Read saving…. No trivia or quizzes yet. Undergraduate Commutative Algebra by Miles Reid. Zvr added it May 17, There are no discussion topics on this book yet. Cyclic surface quotient singularities Graded rings See the Homework.
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