Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure. It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry. Many worked examples and a number of problem (with hints) can be found in the volume. It is also a convenient reference for researchers who use basic commutative algebra.
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The text comes complete with useful examples and exercises. -- Mathematical Reviews
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This introductory chapter concentrates on basic notions and properties concerning Noetherian rings, factorization of elements in a domain, field extensions, symmetric polynomials, trace and norm, free abelian groups of finite rank, and Noetherian modules, which might not be familiar to some readers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
minimal nonzero prime ideal, irreducible algebraic set, ring monomorphisms, factorization into irreducible elements, irreducible plane curve, rational parametrization, affine algebraic sets, multiplicative set, algebraic field extension, repeated zeros, nonzero ideal, maximal member, integral closure, rational mapping, integral basis, integral extension, algebraic element, polynomial ring, prime ideals, ring homomorphism, valuation ring, integral bases, maximal ideal, free abelian group, splitting field Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proposition Let, Proof Exercise, Definition Let, Proof Let, Corollary Let, Lemma Let, Proof Suppose, Proof Note, Proof First New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This introductory chapter concentrates on basic notions and properties concerning Noetherian rings, factorization of elements in a domain, field extensions, symmetric polynomials, trace and norm, free abelian groups of finite rank, and Noetherian modules, which might not be familiar to some readers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
minimal nonzero prime ideal, irreducible algebraic set, ring monomorphisms, factorization into irreducible elements, irreducible plane curve, rational parametrization, affine algebraic sets, multiplicative set, algebraic field extension, repeated zeros, nonzero ideal, maximal member, integral closure, rational mapping, integral basis, integral extension, algebraic element, polynomial ring, prime ideals, ring homomorphism, valuation ring, integral bases, maximal ideal, free abelian group, splitting field Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proposition Let, Proof Exercise, Definition Let, Proof Let, Corollary Let, Lemma Let, Proof Suppose, Proof Note, Proof First New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 9
books:
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- Theory of Numbers by Bonnie M. Stewart in Back Matter
- Number Fields (Universitext) by Daniel A. Marcus in Back Matter
- New Trends in Algebraic Geometry (London Mathematical Society Lecture Note Series) by K. Hulek in Back Matter
- Number theory, Volume 20 (Pure and Applied Mathematics) by Author Unknown on page 101
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter
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