Introduction To The Theory Of Algebraic Numbers And Functions Theory Of Algebraic Numbers And Functions The
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Introduction to the Theory of Algebraic Numbers and Fuctions
Introduction to the Theory of Algebraic Numbers and Fuctions
Algebraic Numbers and Algebraic Functions
This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
The Theory of Algebraic Numbers
Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; Fermat conjecture. 1975 edition.