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Graduate Algebra: Noncommutative View

About this Title

Louis Halle Rowen, Bar-Ilan University, Ramat Gan, Israel

Publication: Graduate Studies in Mathematics
Publication Year: 2008; Volume 91
ISBNs: 978-0-8218-4153-2 (print); 978-1-4704-1802-1 (online)
DOI: https://doi.org/10.1090/gsm/091
MathSciNet review: MR2462400
MSC: Primary 16-01; Secondary 17-01

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Table of Contents

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Front/Back Matter

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Part IV. The structure of rings

• Introduction to the structure of rings
• Chapter 13. Fundamental concepts in ring theory
• Chapter 14. Semisimple modules and rings and the Wedderburn-Artin theorem
• Chapter 15. The Jacobson program applied to left Artinian rings
• Chapter 16. Noetherian rings and the role of prime rings
• Chapter 17. Algebras in terms of generators and relations
• Chapter 18. Tensor products
• Exercises—Part IV

Part V. Representations of groups and Lie algebras

• Introduction to representations of groups and Lie algebras
• Chapter 19. Group representations and group algebras
• Chapter 20. Characters of finite groups
• Chapter 21. Lie algebras and other nonassociative algebras
• Chapter 22. Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups)
• Exercises—Part V

Part VI. Representable algebras

• Introduction to representable algebras
• Chapter 23. Polynomial identities and representable algebras
• Chapter 24. Central simple algebras and the Brauer group
• Chapter 25. Homological algebra and categories of modules
• Chapter 26. Hopf algebras
• Exercises—Part VI