โ Scribed by William Brown
No coin nor oath required. For personal study only.
Cover
Title page
Preface
1. Modules Over Commutative Rings
2. Matrices with Entries from a Commutative Ring
3. The Ideals in M_{nxn}(R)
4. The Rank of a Matrix
5. Linear Equations
6. Minimal Primes and the Radical of an Ideal
7. The Cayley-Hamilton Theorem
8. Resultants
9. Zero Divisors in M_{nxn}(R)
10. Finitely Generated Modules and Local Rings
11. Primary Decompositions in Noetherian Rings
12. Tensor Products
13. Fitting Ideals
14. Principal Ideal Rings
15. The Smith Normal Form of a Matrix
16. The Frobenius Normal Form of a Matrix
17. Eigenvalues and Diagonalizing a Matrix
Appendix A. Partially Ordered Sets and Zorn's Lemma
Appendix B. The Jacobson Radical
Appendix C. Elimination Theory and Bezout's Theorem
Appendix D. The Hilbert-Burch Theorem
Notation
References
Index
๐ SIMILAR VOLUMES
Aims to cover the most important aspects of the theory of matrices whose entries come from a given commutative ring. Essential facts about commutative rings are developed throughout the book, and proofs that follow from concrete matrix calculations are also provided.
