* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed  *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook

Introduction to Plane Algebraic Curves

Science & Math

Kunz, Ernst

Mathematics

Birkhauser

<p>Originally published in 1985, this classic textbook is an English translation of <i>Einführung in die kommutative Algebra und algebraische Geometrie</i>. It presents areas of commutative algebra that are best understood together.</p>

Introduction to Commutative Algebra and Algebraic Geometry (Modern Birkhäuser Classics)

This book is based on a lecture course that I gave at the University of Regensburg. The purpose of these lectures was to explain the role of Kähler differential forms in ring theory, to prepare the road for their application in algebraic geometry, and to lead up to some research problems. The text discusses almost exclusively local questions and is therefore written in the language of commutative alge bra. The translation into the language of algebraic geometry is easy for the reader who is familiar with sheaf theory and the theory of schemes. The principal goals of the monograph are: To display the information contained in the algebra of Kähler differential forms (de Rham algebra) of a commutative algebra, to int- duce and discuss "differential invariants" of algebras, and to prove theorems about algebras with "differential methods". The most important object we study is the module of Kähler differentials n~/R of an algebra SIR. Like the differentials of analysis, differential modules "linearize" problems, i.e. reduce questions about algebras (non-linear problems) to questions of linear algebra. We are mainly interested in algebras of finite type.

Kähler Differentials (Advanced Lectures in Mathematics) (German Edition)

Vieweg+Teubner Verlag

It has been estimated that, at the present stage of our knowledge, one could give a 200 semester course on commutative algebra and algebraic geometry without ever repeating himself. So any introduction to this subject must be highly selective. I first want to indicate what point of view guided the selection of material for this book. This introduction arose from lectures for students who had taken a basic course in algebra and could therefore be presumed to have a knowledge of linear algebra, ring and field theory, and Galois theory. The present text shouldn't require much more. In the lectures and in this text I have undertaken with the fewest possible auxiliary means to lead up to some recent results of commutative algebra and algebraic geometry concerning the representation of algebraic varieties as in tersections of the least possible number of hypersurfaces and- a closely related problem-with the most economical generation of ideals in Noetherian rings. The question of the equations needed to describe an algebraic variety was addressed by Kronecker in 1882. In the 1940s it was chiefly Perron who was interested in this question; his discussions with Severi made the problem known and contributed to sharpening the rei event concepts. Thanks to the general progress of commutative algebra many beautiful results in this circle of questions have been obtained, mainly after the solution of Serre's problem on projective modules. Because of their relatively elementary character they are especially suitable for an introduction to commutative algebra.

Introduction to commutative algebra and algebraic geometry

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Books by Kunz, Ernst

See the best price to sell, buy, or rent books by Kunz, Ernst. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Introduction to Plane Algebraic Curves

Introduction to Commutative Algebra and Algebraic Geometry (Modern Birkhäuser Classics)

Kähler Differentials (Advanced Lectures in Mathematics) (German Edition)

Introduction to commutative algebra and algebraic geometry