Algebraic Theory of Numbers

Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups rings fields ideals quotient rings and quotient fields homomorphisms and isomorphisms modules and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics -- algebraic geometry in particular.<br>This book assumes a knowledge of basic algebra but supplements its teachings with brief clear explanations of integrality algebraic extensions of fields Galois theory Noetherian rings and modules and rings of fractions. It covers the basics starting with the divisibility theory in principal ideal domains and ending with the unit theorem finiteness of the class number and the more elementary theorems of Hilbert ramification theory. Numerous examples applications and exercises appear throughout the text.