Notes on the Theory of Algebraic Numbers
Steve Wright
TL;DR
This paper provides an accessible introduction to algebraic number theory, focusing on elementary concepts and avoiding advanced prerequisites, based on well-known texts and fundamental algebraic structures.
Contribution
It offers a simplified, lecture-based exposition of algebraic number theory suitable for first-semester graduate students without requiring field theory background.
Findings
Clarifies core concepts of algebraic numbers and rings
Provides foundational understanding for further study in number theory
Synthesizes key ideas from classical texts
Abstract
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on the texts of E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer-Verlag, 1981 (English translation by G. Brauer and J. Goldman) and D. Marcus, Number Fields, Springer, 1977.
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Taxonomy
TopicsHistory and Theory of Mathematics · Analytic Number Theory Research · Mathematics and Applications