Algebraic Numbers and Algebraic Functions Artin, E Gordon & Breach, 1967 183d 0677006357

概述:

本书是代数数和代数函数的经典教材，其内容源自普林斯顿1950-1951年所开课程的讲义，此讲义于1967年首次出版。书中第一部分概述了赋值域的一般理论，由此过渡到第二部分中的局部类域理论，然后在第三部分概述单变量的函数场理论（包括黎曼-儒歇定理及其应用）

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.

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