**AMS Chelsea Publishing**

Volume: 358;
1967;
349 pp;
Hardcover

MSC: Primary 11;
**Print ISBN: 978-0-8218-4075-7
Product Code: CHEL/358.H**

List Price: $51.00

Individual Member Price: $45.90

# Algebraic Numbers and Algebraic Functions

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*Emil Artin*

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.

#### Table of Contents

# Table of Contents

## Algebraic Numbers and Algebraic Functions

#### Readership

Graduate students and research mathematicians interested in number theory and algebraic geometry.

#### Reviews

The exposition is (as usual with Artin) quite elegant, and the parallel treatment of number fields and function can be illuminating as well as efficient ... a master of the subject ... It is a true classic in the field.

-- MAA Reviews

Now, after another forty years, and being out of print for the last decades, Artin's classic of timeless beauty has been made available again for new generations of students, teachers, researchers, mathematics historians, and bibliophiles, very much to the benefit of the mathematical community as a whole.

-- Zentralblatt MATH