A First Course in Noncommutative Rings

Автор(ы):Lam T. Y.
06.10.2007
Год изд.:1991
Описание: Однажды на экзамене по математической физике Крэг Хэк не сумел доказать, что собственные функции оператора Лапласа-Бельтрами на единичной сфере S1, отвечающие различным собственным значениям оператора, ортогональны относительно скалярного произведения в L2(S1). С тех пор про варваров рассказывают всякие гадости... Вот приблизительно об этом и эта книга.
Оглавление:
A First Course in Noncommutative Rings — обложка книги.
Chapter 1. Wedderburn-Artin Theory [1]
  § 1. Basic terminology and examples [2]
  § 2. Semisimplicity [26]
  § 3. Structure of semisimple rings [31]
Chapter 2. Jacobson Radical Theory [51]
  § 4. The Jacobson radical [53]
  § 5. Jacobson radical under change of rings [70]
  § 6. Group rings and the J-semisimplicity problem [82]
Chapter 3. Introduction to Representation Theory [107]
  § 7. Modules over finite-dimensional algebras [108]
  § 8. Representations of groups [124]
  § 9. Linear groups [149]
Chapter 4. Prime and Primitive Rings [163]
  § 10. The prime radical; prime and semiprime rings [164]
  § 11. Structure of primitive rings; the Density Theorem [182]
  § 12. Subdirect products and commutativity theorems [203]
Chapter 5. Introduction to Division Rings [213]
  § 13. Division rings [214]
  § 14. Some classical constructions [227]
  § 15. Tensor products and maximal subfields [250]
  § 16. Polynomials over division rings [261]
Chapter 6. Ordered Structures in Rings [275]
  § 17. Orderings and preorderings in rings [276]
  § 18. Ordered division rings [285]
Chapter 7. Local Rings, Semilocal Rings, and Idempotents [293]
  § 19. Local rings [294]
  § 20. Semilocal rings [311]
  § 21. The theory of idempotents [318]
  § 22. Central idempotents and block decompositions [336]
Chapter 8. Perfect and Semiperfect Rings [345]
  § 23. Perfect and semiperfect rings [346]
  § 24. Homological characterizations of perfect and semiperfect rings [358]
  § 25. Principal indecomposables and basic rings [370]
References [381]
Name Index [385]
Subject Index [389]
Формат: djvu
Размер:5372547 байт
Язык:ENG
Рейтинг: 128 Рейтинг
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