Introduction to Plane Algebraic Curves

Treats an introduction to commutative ring theory and algebraic plane curves, with the algebraic facts. This book on plane algebraic curves presents Kunz's conception of teaching topics in commutative algebra together with their applications to algebraic geometry. It includes examples, exercises, figures, and suggestions for further study.

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* 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