From the Preface: 'topics are: valuation theory; theory of polynomial and power series rings (including generalizations to graded rings and modules); local algebra...the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered throughout the exposition. Thus, this volume can be used in part as an introduction to some basic concepts and the arithmetic foundations of algebraic geometry.'
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0 of 7 people found the following review helpful:
3.0 out of 5 stars
Not much to say, really.,
This review is from: Commutative Algebra I (Graduate Texts in Mathematics) (Hardcover)
I bought this to have a matching set with my Volume II.Decent enough for reference, but that's about it. Yeah...that's about it.
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Inside This Book
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First Sentence:
1. Introductory remarks. Homomorphic mappings of rings into fields are very common in commutative algebra and in its applications. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
isolated prime ideal, irredundant primary representation, reduced ramification index, contracted ideal, isomorphic places, simple complete ideals, cendence degree, first kind with respect, chain condition for prime ideals, second kind with respect, leading submodule, derived normal model, whose valuation ring, proper prime ideal, bilinear lemma, associated prime ideal, rational rank, homogeneous coördinates, quadratic transform, prime sequence, unmixed ideal, independent power series, directional form, regular local ring, homogeneous homomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
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1. Introductory remarks. Homomorphic mappings of rings into fields are very common in commutative algebra and in its applications. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
isolated prime ideal, irredundant primary representation, reduced ramification index, contracted ideal, isomorphic places, simple complete ideals, cendence degree, first kind with respect, chain condition for prime ideals, second kind with respect, leading submodule, derived normal model, whose valuation ring, proper prime ideal, bilinear lemma, associated prime ideal, rational rank, homogeneous coördinates, quadratic transform, prime sequence, unmixed ideal, independent power series, directional form, regular local ring, homogeneous homomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hilbert Nullstellensatz New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, Back Matter (1), and Back Matter (2)
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Front Matter, and Back Matter
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) (v. 106) by Joseph H. Silverman in Back Matter (1), and Back Matter (2)
- Galois Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
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