代数学的な数論：手短な入門 Algebraic Number Theory : A Brief Introduction (Textbooks in Mathematics)

Chahal, J. S.

Chapman & Hall（2021/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 152 p.
• 言語 ENG
• 商品コード 9781032010779
• DDC分類 512

Full Description

This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic.The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry.About the AuthorDr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies, he likes to travel and hike. His book, Fundamentals of Linear Algebra, is also published by CRC Press.

Contents

1 Genesis-What is Number Theory?2 Review of the Prerequisite Material 3 Basic Concepts 4 Arithmetic in Relative Extensions 5 Geometry of Numbers 6 Analytic Methods 7 Arithmetic in Galois Extensions 8 Cyclotomic Fields 9 The Kronecker-Weber Theorem 10 Passage to Algebraic Geometry 11 Epilogue-Fermat's Last Theorem Bibliography Index