Author | Lam, T. Y. author |
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Title | A First Course in Noncommutative Rings [electronic resource] / by T. Y. Lam |
Imprint | New York, NY : Springer US, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0406-7 |
Descript | XV, 397p. online resource |
1. Wedderburn-Artin Theory -- ยง1. Basic terminology and examples -- ยง2. Semisimplicity -- ยง3. Structure of semisimple rings -- 2. Jacobson Radical Theory -- ยง4. The Jacobson radical -- ยง5. Jacobson radical under change of rings -- ยง6. Group rings and the J-semisimplicity problem -- 3. Introduction to Representation Theory -- ยง7. Modules over finite-dimensional algebras -- ยง8. Representations of groups -- ยง9. Linear groups -- 4. Prime and Primitive Rings -- ยง10. The prime radical; prime and semiprime rings -- ยง11. Structure of primitive rings; the Density Theorem -- ยง12. Subdirect products and commutativity theorems -- 5. Introduction to Division Rings -- ยง13. Division rings -- ยง14. Some classical constructions -- ยง15. Tensor products and maximal subfields -- ยง16. Polynomials over division rings -- 6. Ordered Structures in Rings -- ยง17. Orderings and preorderings in rings -- ยง18. Ordered division rings -- 7. Local Rings, Semilocal Rings, and Idempotents -- ยง19. Local rings -- ยง20. Semilocal rings -- ยง21. The theory of idempotents -- ยง22. Central idempotents and block decompositions -- 8. Perfect and Semiperfect Rings -- ยง23. Perfect and semiperfect rings -- ยง24. Homological characterizations of perfect and semiperfect rings -- ยง25. Principal indecomposables and basic rings -- References -- Name Index