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Rings, Modules, and Linear Algebra

โœ Scribed by Sean Sather-Wagstaff

Year
2011
Tongue
English
Leaves
84
Series
lecture notes
Edition
version 1 Oct 2011
Category
Library
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โœฆ Table of Contents

Introduction......Page 5
Notation......Page 7
1.2. Additive Abelian Groups......Page 9
2.1. Rings, Homomorphisms, Subrings, and Ideals......Page 13
2.2. Operations on Ideals......Page 17
2.3. Prime Ideals and Maximal Ideals......Page 20
2.4. Quotient Fields......Page 23
2.5. Factorization......Page 24
2.6. Polynomial rings......Page 31
2.7. Factorization in Polynomial Rings......Page 38
3.1. Modules......Page 43
3.2. Module Homomorphisms......Page 44
3.3. Submodules......Page 45
3.4. Generators......Page 48
3.5. Bases, Free Modules, and Vector Spaces......Page 50
3.6. Hom......Page 57
3.7. Exact Sequences......Page 59
3.8. Noetherian Rings and Modules......Page 63
3.9. Modules over Principal Ideal Domains......Page 65
3.10. Left Exactness of Hom......Page 69
3.11. Projective Modules and Injective Modules......Page 71
3.12. Tensor Product......Page 74
3.13. Localization......Page 81

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