中文名: 代數數和代數函數
原名: Algebraic.Numbers.and.Algebraic.Functions
作者: Emil Artin
資源格式: PDF
版本: 掃描版
出版社: American Mathematical Society
書號: 0821840754
發行時間: 2006年
地區: 美國
語言: 英文
簡介:

內容簡介:
本書是代數數和代數函數的經典教材，其內容源自普林斯頓1950-1951年所開課程的講義，此講義於1967年首次出版。書中第一部分介紹了賦值域的一般理論，由此過渡到第二部分中的局部類域理論，然後在第三部分介紹單變量的函數場理論（包括黎曼-儒歇定理及其應用）
Famous Norwegian mathematician Niels Henrik Abel advised that one should "learn from the masters, not from the pupils". When the subject is algebraic numbers and algebraic functions, there is no greater master than Emil Artin. In this classic text, originated from the notes of the course given at Princeton University in 1950-1951 and first published in 1967, one has a beautiful introduction to the subject accompanied by Artin's unique insights and perspectives. The exposition starts with the general theory of valuation fields in Part I, proceeds to the local class field theory in Part II, and then to the theory of function fields in one variable (including the Riemann-Roch theorem and its applications) in Part III. Prerequisites for reading the book are a standard first-year graduate course in algebra (including some Galois theory) and elementary notions of point set topology. With many examples, this book can be used by graduate students and all mathematicians learning number theory and related areas of algebraic geometry of curves.
內容截圖:

目錄:
Part I General Valuation Theory
Part II Local Class Field Theory
Part III Product Formula and Function Fields in One Variable