| Description |
1 online resource (139 pages) |
| Contents |
Cover; Half Title; Title; Copyright; Contents; Introduction; Notation and Terminology; Chapter 1 Rings and Ideals; Rings and ring homomorphisms; Ideals. Quotient rings; Zero-divisors. Nilpotent elements. Units; Prime ideals and maximal ideals; Nilradical and Jacobson radical; Operations on ideals; Extension and contraction; Exercises; Chapter 2 Modules; Modules and module homomorphisms; Submodules and quotient modules; Operations on submodules; Direct sum and product; Finitely generated modules; Exact sequences; Tensor product of modules; Restriction and extension of scalars |
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Exactness properties of the tensor productAlgebras; Tensor product of algebras; Exercises; Chapter 3 Rings and Modules of Fraction; Local properties; Extended and contracted ideals in rings of fractions; Exercises; Chapter 4 Primary Decomposition; Exercise; Chapter 5 Integral Dependence and Valuations; Integral dependence; The going-up theorem; Integrally closed integral domains. The going-down theorem; Valuation rings; Exercises; Chapter 6 Chain Conditions; Exercises; Chapter 7 Noetherian Rings; Primary decomposition in Noetherian rings; Exercises; Chapter 8 Artin Rings; Exercises |
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Chapter 9 Discrete Valuation Rings and Dedekind DomainsDiscrete valuation rings; Dedekind domains; Fractional ideals; Exercises; Chapter 10 Completions; Topologies and completions; Filtrations; Graded rings and modules; The associated graded ring; Exercises; Chapter 11 Dimension Theory; Hilbert functions; Dimension theory of Noetherian local rings; Regular local rings; Transcendental dimension; Exercises; Index |
| Summary |
"First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company."--Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Commutative algebra.
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Commutative rings.
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Commutative algebra
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Commutative rings
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| Form |
Electronic book
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| Author |
Macdonald, I. G
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| ISBN |
9780429962189 |
|
0429962185 |
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9780429493638 |
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0429493630 |
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9780429973253 |
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042997325X |
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9780429984341 |
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0429984340 |
|
