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• catalog abstract ""A First Course in Noncommutative Rings, an outgrowth of the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. By aiming the level of writing at the novice rather than the connoisseur and by stressing the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition."--Jacket.".
• catalog contributor b12149979.
• catalog created "c2001.".
• catalog date "2001".
• catalog date "c2001.".
• catalog dateCopyrighted "c2001.".
• catalog description ""A First Course in Noncommutative Rings, an outgrowth of the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. By aiming the level of writing at the novice rather than the connoisseur and by stressing the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition."--Jacket.".
• catalog description "Includes bibliographical references and indexes.".
• catalog description "Machine generated contents note: CHAPTER 1 -- Wedderburn-Artin Theory --1. Basic Terminology and Examples -- Exercises for 1 -- 2. Semisimplicity -- Exercises for 2 -- 3. Structure of Semisimple Rings -- Exercises for 3 --CHAPTER 2 -- Jacobson Radical Theory --4. The Jacobson Radical -- Exercises for 4 -- 5. Jacobson Radical Under Change of Rings -- Exercises for 5 -- 6. Group Rings and the J-Semisimplicity Problem -- Exercises for 6 --CHAPTER 3 -- Introduction to Representation Theory --7. Modules over Finite-Dimensional Algebras -- Exercises for 7 --8. Representations of Groups -- Exercises for 8 -- 9. Linear Groups -- Exercises for 9 CHAPTER 4 -- Prime and Primitive Rings --10. The Prime Radical; Prime and Semiprime Rings -- Exercises for 10 -- 11. Structure of Primitive Rings; the Density Theorem -- Exercises for 11 -- 12. Subdirect Products and Commutativity Theorems -- Exercises for 12 CHAPTER 5 -- Introduction to Division Rings --13. Division Rings -- Exercises for 13 -- 14. Some Classical Constructions -- Exercises for 14 -- 15. Tensor Products and Maximal Subfields -- Exercises for 15 -- 16. Polynomials over Division Rings -- Exercises for 16 CHAPTER 6 -- Ordered Structures in Rings --17. Orderings and Preorderings in Rings -- Exercises for 17 -- 18. Ordered Division Rings -- Exercises for 18 CHAPTER 7 -- Local Rings, Semilocal Rings, and Idempotents --19. Local Rings -- Exercises for 19 -- 20. Semilocal Rings -- Appendix: Endomorphism Rings of Uniserial Modules -- Exercises for 20 -- 21. Th Theory of Idempotents -- Exercises for 21 -- 22. Central Idempotents and Block Decompositions -- Exercises for 22 -- CHAPTER 8 -- Perfect and Semiperfect Rings --23. Perfect and Semiperfect Rings -- Exercises for 23 -- 24. Homological Characterizations of Perfect and Semiperfect Rings -- Exercises for 24 -- 25. Principal Indecomposables and Basic Rings -- Exercises for 25.".
• catalog extent "xix, 385 p. :".
• catalog identifier "0387951830 (alk. paper)".
• catalog isPartOf "Graduate texts in mathematics ; 131 [bis]".
• catalog issued "2001".
• catalog issued "c2001.".
• catalog language "eng".
• catalog publisher "New York : Springer,".
• catalog subject "512/.4 21".
• catalog subject "Noncommutative rings.".
• catalog subject "QA251.4 .L36 2001".
• catalog tableOfContents "Machine generated contents note: CHAPTER 1 -- Wedderburn-Artin Theory --1. Basic Terminology and Examples -- Exercises for 1 -- 2. Semisimplicity -- Exercises for 2 -- 3. Structure of Semisimple Rings -- Exercises for 3 --CHAPTER 2 -- Jacobson Radical Theory --4. The Jacobson Radical -- Exercises for 4 -- 5. Jacobson Radical Under Change of Rings -- Exercises for 5 -- 6. Group Rings and the J-Semisimplicity Problem -- Exercises for 6 --CHAPTER 3 -- Introduction to Representation Theory --7. Modules over Finite-Dimensional Algebras -- Exercises for 7 --8. Representations of Groups -- Exercises for 8 -- 9. Linear Groups -- Exercises for 9 CHAPTER 4 -- Prime and Primitive Rings --10. The Prime Radical; Prime and Semiprime Rings -- Exercises for 10 -- 11. Structure of Primitive Rings; the Density Theorem -- Exercises for 11 -- 12. Subdirect Products and Commutativity Theorems -- Exercises for 12 CHAPTER 5 -- Introduction to Division Rings --13. Division Rings -- Exercises for 13 -- 14. Some Classical Constructions -- Exercises for 14 -- 15. Tensor Products and Maximal Subfields -- Exercises for 15 -- 16. Polynomials over Division Rings -- Exercises for 16 CHAPTER 6 -- Ordered Structures in Rings --17. Orderings and Preorderings in Rings -- Exercises for 17 -- 18. Ordered Division Rings -- Exercises for 18 CHAPTER 7 -- Local Rings, Semilocal Rings, and Idempotents --19. Local Rings -- Exercises for 19 -- 20. Semilocal Rings -- Appendix: Endomorphism Rings of Uniserial Modules -- Exercises for 20 -- 21. Th Theory of Idempotents -- Exercises for 21 -- 22. Central Idempotents and Block Decompositions -- Exercises for 22 -- CHAPTER 8 -- Perfect and Semiperfect Rings --23. Perfect and Semiperfect Rings -- Exercises for 23 -- 24. Homological Characterizations of Perfect and Semiperfect Rings -- Exercises for 24 -- 25. Principal Indecomposables and Basic Rings -- Exercises for 25.".
• catalog title "A first course in noncommutative rings / T.Y. Lam.".
• catalog type "text".