The CRing Project by Shishir Agrawal
The CRing Project - Table of Contents
Part-I Fundamentals
0. Categories
1. Foundations
2. Fields and Extensions
3. Three important functors
Part-II Commutative algebra
4. The Spec of a ring
5. Noetherian rings and modules
6. Graded and filtered rings
7. Integrality and valuation rings
8. Unique factorization and the class group
9. Dedekind domains
10. Dimension theory
11. Completions
12. Regularity, differentials, and smoothness
Part-III Topics
13. Various topics
14. Homological Algebra
15. Flatness revisited
16. Homological theory of local rings
17. Etale, unramified, and smooth morphisms
18. Complete local rings
19. Homotopical algebra
20. GNU Free Documentation License
What You Will Learn in The CRing Project
The textbook The CRing Project: A Collaborative Open Source Textbook on Commutative Algebra by Shishir Agrawal is a free, open-source resource designed for undergraduate students with a foundation in elementary abstract algebra. Developed collaboratively by Shishir Agrawal and a team of contributors, this textbook offers a modern, accessible approach to commutative algebra while emphasizing conceptual understanding. It is particularly suited for students preparing for advanced topics in algebraic geometry, such as EGA or SGA, but is also valuable for self-learners seeking a rigorous yet approachable introduction.
The textbook is modular, covering key topics including Category Theory, Rings and Modules, Fields and Extensions, Commutative Algebra, and Homological Algebra. Some sections are licensed under the GNU Free Documentation License v1.3, while others use the Creative Commons Attribution 4.0 International (CC BY 4.0) license, allowing educators and students to freely use, adapt, and redistribute the content. The book includes exercises, examples, and historical context to enhance understanding, making abstract concepts more relatable and engaging.
Available in PDF format with LaTeX source code, CRing can be accessed from multiple university servers, including the University of Colorado and University of Rome. As an open-source initiative, it demonstrates the power of collaborative educational projects, providing high-quality, freely available content. Whether for classroom use or independent study, CRing is an invaluable resource for anyone seeking a deep, structured understanding of commutative algebra.
Book Details & Specifications
Title:
The CRing Project by Shishir Agrawal
Publisher:
CRing Project
Year:
2011
Pages:
493
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
CC BY 4.0
Amazon:
N\A
About the Author: Shishir Agrawal
The author
Shishir Agrawal
is a mathematician and educator specializing in commutative algebra and algebraic geometry. He is a faculty member at the University of California, San Diego (UCSD), where he teaches both undergraduate and graduate-level mathematics courses. Dr. Agrawal has contributed to research projects and supervised honors theses, demonstrating a strong commitment to advanced mathematical education. In 2011, he co-authored "The CRing Project: A Collaborative Open Source Textbook on Commutative Algebra", an open-source resource designed to provide a comprehensive and accessible introduction to commutative algebra. His work emphasizes collaborative, freely available educational materials, helping students worldwide explore algebra and algebraic geometry.
Read or Downloadable The CRing Project
Commutative Algebra