The CRing Project: A Collaborative Open Source Textbook on Commutative Algebra by Shishir Agrawal

Book 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

About this book :-
This text 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 Detail :-
Title: The CRing Project: A Collaborative Open Source Textbook on Commutative Algebra 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 Author :-
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.

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