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內容簡介

In spite of the fact that nowadays there are quite a few books on algebraic number theory available to the mathematical community, there seems to be still a strong need for a fundamental work like IIasse's ,,Zahlentheorie". This impression is corroborated by the great number of inquiries the editor received about the date of appearance of the English translation of Hasse's book. One main reason for the unbroken interest in this book lies probably in its vivid presentation of the divisortheoretic approach to algebraic number theory, an approach which was developed by Hasse's former teacher IIensel and further expanded by Hasse himseff. Hasse does not content himself with a mere presentation of the number-theoretic material, but he motivates the basic ideas and questions, comments on them in detail,and points out their connections with neighboring branches of mathematics.

目錄

part ⅰ. the foundations of arithmetic in the rational number field
chapter 1. prime decomposition
function fields
chapter 2. divisibility
function fields
chapter 3. congruences
function fields
the theory of finite fields
chapter 4. the structure of the residue class ring mod m and of the reduced residue class group mod m
1. general facts concerning direct products and direct sums
2. direct decomposition of the residue class ring mod m and of the reduced residue class group mod m
3. the structure of the additive group of the residue class ring mod m
4. on the structure of the residue class ring mod pμ
5. the structure of the reduced residue class group mod pμ
function fields
chapter 5. quadratic residues
1. theory of the characters of a finite abelian group
2. residue class characters and numerical characters mod m
3. the basic facts concerning quadratic residues
4. the quadratic reciprocity law for the legendre symbol
5. the quadratic reciprocity law for the jacobi symbol
6. the quadratic reciprocity law as product formula for the hilbcrt symbol
7. special cases of dirichlet's theorem on prime numbers in reduced residue classes
function field

part ⅱ. the theory of valued fields
chapter 6. the fundamental concepts regarding valuations
1. the definition of a valuation； equivalent valuations
2. approximation independence and multiplicative independence of valuations
3. valuations of the prime field
4. value groups and residue class fields
function fields
chapter 7. arithmetic in a discrete valued field
divisors from an ideal-theoretic standpoint
chapter 8. the completion of a valued field
chapter 9. the completion of a discrete valued field. the lo-adie number fields
function fields
chapter 10. the isomorphism types of complete discrete valued fields with perfect residue class field
1. the multiplicative residue system in the case of prime characteristic
2. the equal-characteristic case with prime characteristic
3. the multiplicative residue system in the p-adic number field
4. witt's vector calculus
5. construction of the general p-adic field
6. the unequal-characteristic case
7. isomorphic residue systems in the case of characteristic 0
8. the isomorphic residue systems for a rational function field
9. the equal-characteristic case with characteristic 0
chapter 11. prolongation of a discrete valuation to a purely transcendental extension
chapter 12. prolongation of the valuation of a complete field to a finitealgebraic extension
1. the proof of existence
2. the proof of completeness
3. the proof of uniqueness
chapter 13. the isomorphism types of complete archimedean valued fields
chapter 14. the structure of a finite-algebraic extension of a complete discrete valued field
1. embedding of the arithmetic
2. the totally ramified case
3. the unramified case with perfect residue class field
4. the general case with perfect residue class field
5. the general case with finite residue class field
chapter 15. the structure of the multiplicative group of a complete discrete valued field with perfect residue class field of prime characteristic
1. reduction to the one-unit group and its fundamental chain of subgroups
2. the one-unit group as an abelian operator group
3. the field of nth roots of unity over a p-adic number field
4. the structure of the one-unit group in the equal-charaeteristie case with finite residue class field
5. the structure of the one-unit group in the p-adie case
6. construction of a system of fundamental one-units in the p-adic case
7. the one-unit group for special p-adic number fields
8. comparison of the basis representation of the multiplieative group in the p-adic case and the archimedean case
chapter 16. the tamely ramified extension types of a complete discrete valued field with finite residue class field of characteristic p
chapter 17. the exponential function， the logarithm， and powers in a complete non-archimedean valued field of characteristic 0
1. integral power series in one indeterminate over an arbitrary field
2. integral power series in one variable in a complete non-archimedean valued field
3. convergence
4. functional equations and mutual relations
5. the discrete case
6. the equal-characteristic case with characteristic 0
chapter 18. prolongation of the valuation of a non-complete field to a finite-algebraic extension
1. representations of a separable finite-algebraic extension over an arbitrary extension of the ground field
2. the ring extension of a separable finite-algebraic extension by an arbitrary ground field extension， or the tensor product
of the two field extensions
3. the characteristic polynomial
4. supplements for inseparable extensions
5. prolongation of a valuation
6. the discrete case
7. the archimedean case

part ⅲ. the foundations of arithmetic in algebraic number fields
chapter 19. relations ]3etween the complete system of valuations and the arithmetic of the rational number field
1. finiteness properties
2. characterizations in divisibility theory
3. the product formula for valuations
4. the sum formula for the principal parts function fields
the automorphisms of a rational function field
chapter 20. prolongation of the complete system of valuations to a finitealgebraic extension
function fields
concluding remarks
chapter 21. the prime spots of an algebraic number field and their completions
function fields
chapter 22. decomposition into prime divisors， integrality， and divisibility
1. the canonical homomorphism of the multiplicative group into the divisor group
2. embedding of divisibility theory under a finite-algebraic extension
3. algebraic characterization of integral algebraic numbers
4. quotient representation
function fields
constant fields， constant extensions
chapter 23. congruences
1. ordinary congruence
2. multiplicative congruence
function fields
chapter 24. the multiples of a divisor
1. field bases
2. the ideal property， ideal bases
3. congruences for integral elements
4. divisors from the ideal-theoretic standpoint
5. further remarks concerning divisors and ideals
function fields
constant fields for p. characterization of prime divisors by homomorphisms. decomposition law under an algebraic constant extension
the rank of the module of multiples of a divisor
chapter 25. differents and discriminants
1. composition formula for the trace and norm. the divisor trace
2. definition of the different and diseriminant
3. theorems on differents and discriminants in the small
4. the relationship between differents and discriminants in the small and in the large
5. theorems on differents and discriminants in the large
6. common inessential discriminant divisors
7. examples
function fields
the number of first-degree prime divisors in the case of a finite constant field
differentials
the riemann-roch theorem and its consequences
disclosed algebraic function fields
chapter 26. quadratic number fields
1. generation in the large and in the small
2. the decomposition law
3. discriminants， integral bases
4. quadratic residue characters of the discriminant of an arbitrary algebraic number field
5. the quadratic number fields as class fields
6. the hilbert symbol as norm symbol
7. the norm theorem
8. a necessary condition for principal divisors. genera
chapter 27. cyelotomic fields
1. generation
2. the decomposition law
3. discriminants， integral bases
4. the quadratic number f 數論 下載 mobi epub pdf txt 電子書 格式

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一個老是受班上同學欺負的瘦弱小男孩，因為擁有一種特殊能力而強大：他能“ 偷彆人的影子” ，因而能看見他人心事，聽見人們心中不願意說齣口的秘密。他開始成為需要幫助者的心靈夥伴，為每個偷來的影子點亮生命的小小光芒。[1] 某年燦爛的夏天，他在海邊邂逅一位又聾又啞的女孩。他該如何用自己的能力幫助她？他將如何信守與她共許的承諾？[2] [3]不知道姓氏的剋蕾兒。一個會用風箏寫齣“我想你”的女孩啊，讓人永遠都忘不瞭。[3] 一段纏綿多年的愛戀，一段進行中的不完美愛情。故事溫柔風趣，輕盈優雅，能讓你我真正感受到心跳的愛情療愈小說。一個愛與友情盛開的美麗世界，在此，想象力超越瞭一切日常生活及人際關係。一本關於童年追憶、關於深藏在成年人內心深處夢想的小說。馬剋．李維一貫的寫作風格，國外齣版社定義本書為“溫柔又風趣”。容易貼近颱灣女性讀者的心。有浪漫的愛情元素、父母親子課題、朋友相挺的義氣，迎閤大眾市場。愛情場景刻畫細緻，對白浪漫感人，尤其結局會讓女性感動。母子親情的刻畫很催淚。跟《那些我們沒談過的事》寫法相似，有不美滿傢庭長大的主角、有貼心好友、一段多年的愛戀、一段進行中的不完美愛情……最後，多年的情人浪漫復閤。 2作品目錄 楔子 001·我的童年就在那裏，帶點憂愁又有點悲痛，在這外省的小城市裏，我拼命等著伊麗莎白垂憐而看我一眼，在絕望中等待長大。影子的秘密 005·為每一個你所偷來的影子找到點亮生命的小小光芒，為它們找迴隱匿的記憶拼圖，這便是我們對你的全部請托。海灘上的剋蕾兒 071·她凝視著我，漾齣一朵微笑，並且在紙上寫下：“你偷走瞭我的影子，不論你在哪裏，我都會一直想著你。” 呂剋的夢想 089·生命中某些珍貴的片刻，其實都來自於一些微不足道的小事。如果我今晚沒有留下來，我想我永遠不會與母親有此番深談。與母親一起離開閣樓後，我最後一次踱迴天窗底下，默默感謝我的影子。蘇菲的傷 131·我隻是你生活裏的一個影子，你卻在我的生命裏占有重要地位。如果我隻是個單純的過客，為何要讓我闖入你的生活?我韆百次想過要離開你，但僅憑一己之力我做不到。 偷影子的人被喚迴的記憶 173·不知道姓氏的剋蕾兒。這就是你在我生命裏的角色，我童年時的小女孩，今日蛻變成瞭女人，一段青梅竹馬的迴憶，一個時間之神沒有應允的願望。用風箏寫下的思念 201·一個會用風箏嚮你寫齣“我想你”的女孩啊，真讓人永遠都忘不瞭她。緻謝 / 221 他們眼中《偷影子的人》/ 224 3點評鑒賞 《偷影子的人》是馬剋·李維的第10部作品，該書在法國首印45萬冊，位列全年銷量排行榜的總冠軍，法國媒體驚嘆：“銷售得比影子消失的速度還快！”這部作品完美展現瞭馬剋·李維溫柔風趣的寫作風格，有催人淚下的親情、浪漫感人的愛情和不離不棄的友情，清新浪漫的氣息和溫柔感人的故事相互交織，帶給讀者笑中帶淚的閱讀感受，是一部喚醒童年迴憶和內心夢想的溫情療愈小說。

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