作者：哈塞(Helmut Hasse)
页数：638
出版社：世界图书出版公司
出版日期：2010
ISBN：9787510027352
电子书格式：pdf/epub/txt
内容简介
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.
目录
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
节选
《数论》内容简介：In spite of the fact that nowadays there are quite a few books on algebraic numbertheory available to the mathematical community, there seems to be still a strongneed for a fundamental work like Hasse’s ,Zahlentheorie”. This impression iscorroborated by the great number of inquiries the editor received about the dateof appearance of the English translation of Hasse’s book. One main reason for theunbroken interest in this book lies probably in its vivid presentation of the divisor-theoretic approach to algebraic number theory, an approach which was developedby Hasse’s former teacher Hensel and further expanded by Hasse himself. Hassedoes not content himself with a mere presentation of the number-theoretic mate-rial, but he motivates the basic ideas and questions, comments on them in detail,and points out their connections with neighboring branches of mathematics. In preparing the English edition of Hasse’s “Number Theory”, I tried to pre-serve as much as possible the unique style and features of the book, even at therisk of using a partly insufficient or somewhat clumsy English. In particular,I kept the original notation of the book thus following the requirements stipulatedby Hasse. This means, e.g., that [- denotes the ring of rational integers, P thefield of rational numbers, P the field of real numbers, Pp the p-adic completionof P, and Z the field of complex numbers.
