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Book Categories |
Preface | ||
1 | Modules Over Commutative Rings | 1 |
2 | Matrices with Entries from a Commutative Ring | 10 |
3 | The Ideals in M[subscript nxn](R) | 20 |
4 | The Rank of a Matrix | 28 |
5 | Linear Equations | 35 |
6 | Minimal Primes and the Radical of an Ideal | 52 |
7 | The Cayley-Hamilton Theorem | 62 |
8 | Resultants | 78 |
9 | Zero Divisors in M[subscript nxn](R) | 105 |
10 | Finitely Generated Modules and Local Rings | 110 |
11 | Primary Decompositions in Noetherian Rings | 123 |
12 | Tensor Products | 135 |
13 | Fitting Ideals | 149 |
14 | Principal Ideal Rings | 175 |
15 | The Smith Normal Form of a Matrix | 180 |
16 | The Frobenius Normal Form of a Matrix | 204 |
17 | Eigenvalues and Diagonalizing a Matrix | 214 |
Appendix A. Partially Ordered Sets and Zorn's Lemma | 230 | |
Appendix B. The Jacobson Radical | 233 | |
Appendix C. Elimination Theory and Bezout's Theorem | 242 | |
Appendix D. The Hilbert-Burch Theorem | 260 | |
Notation | 267 | |
References | 275 | |
Index | 277 |
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Add Matrices over Commutative Rings, 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 al, Matrices over Commutative Rings to the inventory that you are selling on WonderClubX
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Add Matrices over Commutative Rings, 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 al, Matrices over Commutative Rings to your collection on WonderClub |