Groups, Rings, Modules (Dover Books on Mathematics)

Book Details

• Author: Maurice Auslander

• Publisher: Dover

• Binding: Paperback

• Number of Pages: 480

• Release Date: 21-05-2014

• ISBN: 9780486490823

• Dimensions: 9.1 x 6.1 x 1.1 inches

• Languages: English

About the Book

Title: Introduction to Commutative Algebra
This classic monograph by Maurice Auslander is aimed at advanced undergraduates and graduate students with a foundation in sets, groups, rings, and vector spaces. It offers a comprehensive exploration of commutative algebra, a key branch of mathematics, and is an essential text for those studying the topic at an advanced level.

Key Features:

• Four-Part Structure: The book is organized into four parts, each focusing on a distinct area of commutative algebra:

  1. Sets and Maps, Monoids, Groups, Categories, and Rings: The first part establishes the foundational concepts of commutative algebra, essential for building a deeper understanding.

  2. Factorization Domains, Modules, Semisimple Rings: This section dives into unique factorization domains, module theory, and semisimple rings, offering advanced insights into algebraic structures.

  3. Localization, Tensor Products, Principal Ideal Domains: Part three covers key topics such as localization, tensor products, and the applications of the fundamental theorem of algebra.

  4. Field Extensions and Dedekind Domains: The final part examines algebraic field extensions and Dedekind domains, critical for understanding algebraic number theory.

• Exercises: Each chapter concludes with a series of exercises designed to test comprehension and help readers apply the material they have learned.

• Historical Context: This work, originally published in 1974, is now republished by Dover Publications. It stands as an authoritative text in the field, retaining its relevance even decades after its original release.

About the Author:

Maurice Auslander (1926–1994) was a Professor of Mathematics at Brandeis University. He is renowned for his contributions to commutative algebra and module theory. His expertise and clear exposition make this text an invaluable resource for students and researchers in algebra. David A. Buchsbaum, also from Brandeis University, contributed to the development of the text.

Why This Book is Important:

This monograph is a cornerstone of commutative algebra literature, offering an in-depth, methodical treatment of the subject. It helps bridge the gap between undergraduate-level mathematics and the more advanced theoretical work in algebraic geometry and number theory.

The book is ideal for anyone seeking to understand the nuances of algebraic structures, offering a blend of theoretical exposition with practical exercises. Whether you are a student preparing for exams, a researcher exploring commutative algebra, or a self-study enthusiast, "Introduction to Commutative Algebra" provides the foundational knowledge necessary for advancing in the field of mathematics.

Introduction to Commutative Algebra is a must-have reference for students of mathematics and researchers interested in commutative algebra, module theory, and related fields.