This book will be particularly valuable to the American student because it covers material that is not available in any other textbooks or monographs. The subject of the book is not restricted to commutative algebra developed as a pure discipline for its own sake, nor is it aimed only at algebraic geometry where the intrinsic geometry of a general n-dimensional variety plays the central role. Instead, this book is developed around the vital theme that certain areas of both subjects are best understood together. This link between the two subjects, forged in the nineteenth century, built further by Krull and Zariski, remains as active as ever. In this book, the reader will find as the same time a leisurely and clear exposition of the basic definitions and results in both algebra and geometry, as well as an cxposition of the important recent progress fue to Quillen-Suslin, Evans-Eisenbud, Szpiro, Mohan Kumar and others. The ample exercises are another excellent feature. Professor Kunz has filled a longstanding need for an introduction to commutative algebra and algebraic geometry that emphasizes the concrete elementary nature of objects with which both subjects began.
--This text refers to an alternate
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Editorial Reviews
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"An excellent text for a student who wants to learn the basic facts from commutative algebra and algebraic geometry... Many examples and exercises complete the text."
—REVUE ROUMANIE DE MATHÉMATIQUES PURES ET APPLIQUÉES
"An excellent introduction to the subject... The center of gravity lies in commutative algebra, and this book can serve as a preparation for more advanced topics. The presentation is very clear and the theory is accompanied by numerous interesting exercises...This is a highly recommended text for students and lecturers."
—MATHEMATICA
"Outrageous as it may sound this is the first really introductory book written about the new algebraic geometry of the sixties. At last something that we can give our students without cautionary words, and where we ourselves can learn basic concepts that cut across the party lines of mathematics."
—Gian-Carlo Rota, formerly MIT
--This text refers to an alternate Hardcover edition.Language Notes
Text: English, German (translation)
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First Sentence:
In this chapter affine algebraic varieties are introduced as the solution sets of systems of algebraic equations, and projective varieties are introduced as the solution sets in projective space of systems of algebraic equations involving only homogeneous polynomials. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
prime ideal chain, geometric tangent cone, relevant prime ideals, minimal prime divisor, conormal module, regular parameter system, positively graded ring, minimal generating system, many minimal prime ideals, reduced primary decomposition, integral ring extension, principal ideal theorem, regular local ring, regular locus, fiber sum, complete intersection, vanishing ideal, finite projective dimension, projective case, homogeneous prime ideals, projective closure, graded case, principal ideal ring, affine algebra, minimal free resolution Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cohen Macaulay, Hilbert's Nullstellensatz, Mohan Kumar, Noether Normalization Theorem, Snake Lemma, Serre's Splitting-off Theorem, Exercises Let, Krull's Intersection Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter affine algebraic varieties are introduced as the solution sets of systems of algebraic equations, and projective varieties are introduced as the solution sets in projective space of systems of algebraic equations involving only homogeneous polynomials. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
prime ideal chain, geometric tangent cone, relevant prime ideals, minimal prime divisor, conormal module, regular parameter system, positively graded ring, minimal generating system, many minimal prime ideals, reduced primary decomposition, integral ring extension, principal ideal theorem, regular local ring, regular locus, fiber sum, complete intersection, vanishing ideal, finite projective dimension, projective case, homogeneous prime ideals, projective closure, graded case, principal ideal ring, affine algebra, minimal free resolution Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cohen Macaulay, Hilbert's Nullstellensatz, Mohan Kumar, Noether Normalization Theorem, Snake Lemma, Serre's Splitting-off Theorem, Exercises Let, Krull's Intersection Theorem 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 19
books:
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34
books
cite this book:
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- Algebraic Geometry by Shreeram S. Abhyankar in Back Matter (1), and Back Matter (2)
- Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne on page 140, and Back Matter
- Algebraic Space Curves (Seminaire de mathematiques superieures--ete 1970, 43) by Shreeram Shankar Abhyankar in Back Matter
- Principles of Algebraic Geometry by Phillip Griffiths in Back Matter
- Methods of Algebraic Geometry: Volume 1 (Cambridge Mathematical Library) by W. V. D. Hodge in Back Matter
See all 19 books this book cites
- The Fermat Proof by C. J. Mozzochi in Back Matter
- Serre's Problem on Projective Modules by T.Y. Lam in Back Matter
- Monomial Algebras (Chapman & Hall/CRC Pure and Applied Mathematics) by Rafael Villarreal in Back Matter
- Rings, Modules, Algebras, and Abelian Groups (Lecture Notes in Pure and Applied Mathematics) by Alberto Facchini on page 424
- The Concise Handbook of Algebra by A.V. Mikhalev in Back Matter
See all 34 books citing this book
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