Algebratxt,chm,pdf,epub,mobi下载 作者: Serge Lang 出版社: Springer 出版年: 2002 页数: 914 定价: USD 79.95 装帧: Hardcover 丛书: Graduate Texts in Mathematics ISBN: 9780387953854 内容简介 · · · · · ·Book Description "Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." NOTICES OF THE AMS "The author has an impressive knack for presenting the important and interesting ideas of algebra in ... 作者简介 · · · · · ·Serge Lang (May 19, 1927–September 12, 2005) was a French-born American mathematician. He was known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group. He was born in Paris in 1927, and moved with his family to California as a teenager. He graduated from CalTech in 1946, and received a doctor... 目录 · · · · · ·Part One The Basic Objects of AlgebraChapter 1 Groups 1. Monoids 2. Groups 3. Normal subgroups 4. Cyclic groups · · · · · ·() Part One The Basic Objects of Algebra Chapter 1 Groups 1. Monoids 2. Groups 3. Normal subgroups 4. Cyclic groups 5. Operations of a group on a set 6. Sylow subgroups 7. Direct sums and free abelian groups 8. Finitely generated abelian groups 9. The dual group 10. Inverse limit and completion 11. Categories and functors 12. Free groups Chapter 2 Rings 1. Rings and homomorphisms 2. Commutative rings 3. Polynomials and group rings 4. Localization 5. Principal and factorial rings Chapter 3 Modules Chapter 4 Polynomlals Part Two Algebraic Equations Chapter 5 Algebralc Extensions Chapter 6 Galois Theory Chapter 7 Extensions of Rings Chapter 8 Transcendental Extensions Chapter 9 Algebraic Spaces Chapter 10 Noetherial Rings and Modules Chapter 11 Real Fields Chapter 12 Absolute Values Part Three Liear Alebar and Reqresentations Chapter 13 Matrices and Linear Maps Chapter 14 Representatlon of One Endomorphism Chapter 15 Structure of Bilinear Forms Chapter 16 The Tensor Product Chapter 17 Smisimplicity Chapter 18 Representations of Finite Groups Chapter 19 The Alternating Product Part Four Homological Algebra Chapter 20 General Homology Theory Chapter 21 Finite Free Resolutions Appendix 1 The Transcendence of e and Appendix 2 Some Set Theory Bibliography Index · · · · · · () |
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