algebraic number theory

Algebraic, Number Theoretic, and Topological Aspects of Ring Theory【電子書籍】【中古】【輸入品 未使用】The Theory of Algebraic Number FieldsElementary Number Theory An Algebraic Approach【電子書籍】 Ethan D. BolkerContributions in Analytic and Algebraic Number Theory Festschrift for S. J. Patterson【電子書籍】Algebraic Theory of Quadratic Numbers【電子書籍】 Mak TrifkoviAlgebraic Number Theory【電子書籍】 Richard A. MollinThe Theory of Algebraic Numbers【電子書籍】 Harold G. Diamond(出版社)Springer Verlag Algebraic Number Theory 1冊 978-3-319-07544-0Algebraic Number Theory A Brief Introduction【電子書籍】 J.S. ChahalAlgebraic Number Theory【電子書籍】 Frazer JarvisAlgebraic Theory of Numbers Translated from the French by Allan J. Silberger【電子書籍】 Pierre SamuelAlgebraic Number Theory【電子書籍】 Edwin WeissA Textbook of Algebraic Number Theory【電子書籍】 Sudesh Kaur Khanduja
 

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  • <p>This volume has been curated from two sources: presentations from the <em>Conference on Rings and Polynomials</em>, Technische Universit?t Graz, Graz, Austria, July 19 ?24, 2021, and papers intended for presentation at the <em>Fourth International Meeting on Integer-valued Polynomials and Related Topics</em>, CIRM, Luminy, France, which was cancelled due to the pandemic. The collection ranges widely over the algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Two areas of particular note are topological methods in ring theory, and integer valued polynomials. The book is dedicated to the memory of Paul-Jean Cahen, a coauthor or research collaborator with some of the conference participants and a friend to many of the others. This collection contains a memorial article about Paul-Jean Cahen, written by his longtime research collaborator and coauthor Jean-Luc Chabert.</p>画面が切り替わりますので、しばらくお待ち下さい。 ※ご購入は、楽天k...
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  • 【中古】【輸入品・未使用】The Theory of Algebraic Number Fields【メーカー名】Springer【メーカー型番】【ブランド名】Springer【商品説明】The Theory of Algebraic Number Fields当店では初期不良に限り、商品到着から7日間は返品を 受付けております。こちらは海外販売用に買取り致しました未使用品です。買取り致しました為、中古扱いとしております。他モールとの併売品の為、完売の際はご連絡致しますのでご了承下さい。速やかにご返金させて頂きます。ご注文からお届けまで1、ご注文⇒ご注文は24時間受け付けております。2、注文確認⇒ご注文後、当店から注文確認メールを送信します。3、配送⇒当店海外倉庫から取り寄せの場合は10〜30日程度でのお届けとなります。国内到着後、発送の際に通知にてご連絡致します。国内倉庫からの場合は3〜7日でのお届けとなります。 ※離島、北海道、九州、沖縄は遅れる場合がございます。予めご了承下さい。お電話でのお問合せは少人数で運営の為受け付けておりませんので、メールにてお問合せお願い致します。営業時間 月〜金 10:00〜17:00お客様都合によるご注文後のキャンセル・返品はお受けしておりませんのでご了承下さい。
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  • <p>This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and the Fermat conjecture for exponents three and four. The text contains abundant numerical examples and a particularly helpful collection of exercises, many of which are small research problems requiring substantial study or outside reading. Some problems call for new proofs for theorems already covered or for inductive explorations and proofs of theorems found in later chapters.<br /> Ethan D. Bolker teaches mathematics and computer science at the University of Massachusetts, Boston.</p>画面が切り替わりますので、しばらくお待ち下さい。 ※ご購入は、楽天kobo商品ページからお願いします。※切り替わらない場合は、こちら をクリックして下さい。 ※このページからは注文できません。
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  • <p>The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed from lectures given at the "International Conference on the Occasion of the 60th Birthday of S. J. Patterson", held at the University G?ttingen, July 27-29 2009. Many of the included chapters have been contributed by invited participants.</p> <p>This volume presents and investigates the most recent developments in various key topics in analytic number theory and several related areas of mathematics.</p> <p>The volume is intended for graduate students and researchers of number theory as well as applied mathematicians interested in this broad field.</p>画面が切り替わりますので、しばらくお待ち下さい。 ※ご購入は、楽天kobo商品ページからお願いします。※切り替わらない場合は、こちら をクリックして下さい。 ※このペー...
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  • <p>By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes.</p> <p>The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic f...
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  • <p>Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.</p>画面が切り替わりますので、しばらくお待ち下さい。 ※ご購入は、楽天kobo商品ページからお願いします。※切り替わらない場合は、こちら をクリックして下さい。 ※このページからは注文できません。
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  • <p>Detailed proofs and clear-cut explanations provide an excellent introduction to the elementary components of classical algebraic number theory in this concise, well-written volume.<br /> The authors, a pair of noted mathematicians, start with a discussion of divisibility and proceed to examine Gaussian primes (their determination and role in Fermat's theorem); polynomials over a field (including the Eisenstein irreducibility criterion); algebraic number fields; bases (finite extensions, conjugates and discriminants, and the cyclotomic field); and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture (concluding with discussions of Pythagorean triples, units in cyclotomic fields, and Kummer's theorem).<br /> In addition to a helpful list of symbols and ...
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  • (出版社)Springer Verlag Algebraic Number Theory 1冊●著者:Jarvis, Frazer●シリーズ名:Springer Undergraduate Mathematics Series●頁数他:292 p.●装丁:Paper●版次:2014th ed.●出版社:Springer Verlag●発行日:2014/7/4
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  • <p>This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic.</p> <p>The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry.</p> <p>About the Author</p> <p>Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins Univers...
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  • <p>This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform.</p> <p>The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.</p>画面が切り替わりますの...
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  • <p>Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics ー algebraic geometry, in particular.<br /> This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Galois theory, Noetherian rings and modules, and rings of fractions. It covers the basics, starting with the divisibility theory in principal ideal domains and ending with the unit theorem, finiteness of the class number, and the more elementary theorems of Hilbert ramification theory. Numerous examples, applications, and exercises appear throughout the text.</p>画面が切り替わりま...
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  • <p>Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).<br /> Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract techniques constitute the primary focus. Topics include introductory materials on elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.<br /> Subjects correspond to those usually covered in a one-semester, graduate level course in algebraic number theory, making this book ideal either for classroom...
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  • <p>This self-contained and comprehensive textbook of algebraic number theory is useful for advanced undergraduate and graduate students of mathematics. The book discusses proofs of almost all basic significant theorems of algebraic number theory including Dedekind’s theorem on splitting of primes, Dirichlet’s unit theorem, Minkowski’s convex body theorem, Dedekind’s discriminant theorem, Hermite’s theorem on discriminant, Dirichlet’s class number formula, and Dirichlet’s theorem on primes in arithmetic progressions. A few research problems arising out of these results are mentioned together with the progress made in the direction of each problem.</p> <p>Following the classical approach of Dedekind’s theory of ideals, the book aims at arousing the reader’s interest in the current research being held in the subject area. It not only proves basic results but pairs them with recent developments, making the book relevant and thought-provoking. Historical notes are given at various ...
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