數論

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.

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