This classic book gives a thorough introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. It also provides a comprehensive look at recent research. For experimental number theoreticians, the authors developed new methods and obtained new results of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.
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."..it fills a void in the literature. The book makes it less difficult for one to learn the constructive aspects of algebraic number theory." Charles. J. Parry, Mathematical Reviews
Book Description
Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.
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Inside This Book
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First Sentence:
Algebraic numbers are defined as complex numbers x satisfying an algebraic equation of the form Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
solving norm equations, unital commutative ring, invertible relative, minimal splitting field, prime ideal factorization, quintic fields, monic separable polynomial, sextic fields, exponential valuation, discriminant ideal, partial endomorphisms, invertible with respect, splitting ring, quartic fields, convex body theorem, unital ring, elementary ideals, distinct monic irreducible polynomials, equation ring, purely inseparable extension, root generators, exponent ideal, primitive idempotents, orthogonal idempotents, prime ideals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Any, Proof Without New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Algebraic numbers are defined as complex numbers x satisfying an algebraic equation of the form Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
solving norm equations, unital commutative ring, invertible relative, minimal splitting field, prime ideal factorization, quintic fields, monic separable polynomial, sextic fields, exponential valuation, discriminant ideal, partial endomorphisms, invertible with respect, splitting ring, quartic fields, convex body theorem, unital ring, elementary ideals, distinct monic irreducible polynomials, equation ring, purely inseparable extension, root generators, exponent ideal, primitive idempotents, orthogonal idempotents, prime ideals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Any, Proof Without 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 13
books:
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48
books
cite this book:
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- Disquisitiones Arithmeticae by Carl F. Gauss on page 44, page 172, and Back Matter
- Number Theory by Helmut Hasse in Back Matter (1), and Back Matter (2)
- Gesammelte Abhandlungen. Erster Band: Zahlentheorie (AMS Chelsea Publishing) by David Hilbert in Back Matter
- Abstract Algebra: A Computational Approach by Charles C. Sims in Back Matter
- Number Fields (Universitext) by Daniel A. Marcus in Back Matter
See all 13 books this book cites
- Computational Number Theory: Proceedings of the Colloquium on Computational Number Theory Held at Kossuth Lajos University, Debrecen (Hungary), Sep by Michael E. Pohst on page 182, page 190, and page 330
- Digital Signal Processing Algorithms: Number Theory, Convolution, Fast Fourier Transforms, and Applications (Computer Science & Engineering) by Hari Krishna Garg on page 120, and page 331
- Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications) by Charles C. Sims in Front Matter, and Back Matter
- Algorithmic Number Theory: Third International Symposium, ANTS-III, Portland, Orgeon, USA, June 21-25, 1998, Proceedings (Lecture Notes in Computer Science) by Joe P. Buhler on page 337, and page 606
- Software Process Technology: 5th European Workshop, EWSPT '96, Nancy, France, October 9 - 11, 1996. Proceedings (Lecture Notes in Computer Science) by Carlo Montangero on page 148, and page 296
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