Free Download Commutative Algebra: An Introduction
English | 2016 | ISBN: 1944534601 | 243 Pages | EPUB (True) | 8 MB
The purpose of this book is twofold: to present some basic ideas in commutative algebra and algebraic geometry and to introduce some interesting topics of current research centered around the themes of Gröbner bases, resultants and syzygies. There are many good introductory texts on commutative algebra and algebraic geometry, and the intention of this book is to be a supplement to those texts with the aim of pointing the reader toward possible future research directions. The presentation of the material combines definitions and proofs with an emphasis on concrete examples. The authors illustrate the use of software such as Mathematica and Singular. The design of the text in each chapter consists of two parts: the fundamentals and the applications, which make it suitable for courses of various lengths, levels, and topics based on the mathematical background of the students. The fundamentals portion of the chapter is intended for an average graduate student to read with minimal outside assistance, and to learn some of the most useful tools in commutative algebra. The applications of the chapter are to provide a glimpse of the advanced mathematical research where the topics and results are related to the material presented in the fundamentals. In the applications, we allow ourselves to present a number of results from a wide range of sources without detailed proofs. The applications portion of the chapter is suitable for a reader who knows a little commutative algebra and algebraic geometry already, and serves as a guide to some interesting research topics.This book should be thought of as an introduction to more advanced texts and research topics. The novelty of this book is that the material presented here is a unique combination of the essential methods and the current research results. The goal is to equip readers with the fundamental classical algebra and geometry tools, ignite their research interests, and initiate some potential research projects in the related areas.