非交换环初级教程

preface to the second edition preface to the first edition notes to the reader 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

preface to the second edition preface to the first edition notes to the reader 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-semisimplicjty 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, semilocai rings, and idempotents 19. local rings exercises for 19 20. semilocal rings appendix: endomorphism rings of uniserial modules exercises for 20 21. th theory ofidempotents 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. homoiogical characterizations of perfect and semiperfect rings exercises for 24 25. principal indecomposables and basic rings exercises for 25 references name index subject index

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. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson' s theory of the radical, representation theory of groups and algebras, prime and semiprime rings, primitive and semiprimitive rings, division rings, ordered rings, local and semilocal rings, perfect and semiperfect rings, and so forth. 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.