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Matrices over Commutative Rings Book

Matrices over Commutative Rings
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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
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  • Matrices over Commutative Rings
  • Written by author William C. Brown
  • Published by CRC Press, 11/28/1992
  • 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
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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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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

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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

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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

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