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Graduate Algebra: Commutative View
About this Title
Louis Halle Rowen, Bar-Ilan University, Ramat Gan, Israel
Publication: Graduate Studies in Mathematics
Publication Year:
2006; Volume 73
ISBNs: 978-0-8218-0570-1 (print); 978-1-4704-1152-7 (online)
DOI: https://doi.org/10.1090/gsm/073
MathSciNet review: MR2242311
MSC: Primary 13-01; Secondary 11-01
Table of Contents
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Front/Back Matter
Chapters
Part I. Modules
- Chapter 1. Introduction to modules and their structure theory
- Chapter 2. Finitely generated modules
- Chapter 3. Simple modules and composition series
- Exercises—Part I
Part II. Affine algebras and Noetherian rings
- Introduction to Part II
- Chapter 4. Galois theory of fields
- Chapter 5. Algebras and affine fields
- Chapter 6. Transcendence degree and the Krull dimension of a ring
- Chapter 7. Modules and rings satisfying chain conditions
- Chapter 8. Localization and the prime spectrum
- Chapter 9. The Krull dimension theory of commutative Noetherian rings
- Exercises—Part II
Part III. Applications to geometry and number theory