An Introduction to Commutative Algebra and Number Theory

· CRC Press

About this ebook

An Introduction to Commutative Algebra and Number Theory is an elementary introduction to these subjects. Beginning with a concise review of groups, rings and fields, the author presents topics in algebra from a distinctly number-theoretic perspective and sprinkles number theory results throughout his presentation. The topics in algebra include polynomial rings, UFD, PID, and Euclidean domains; and field extensions, modules, and Dedekind domains.

In the section on number theory, in addition to covering elementary congruence results, the laws of quadratic reciprocity and basics of algebraic number fields, this book gives glimpses into some deeper aspects of the subject. These include Warning's and Chevally's theorems in the finite field sections, and many results of additive number theory, such as the derivation of LaGrange's four-square theorem from Minkowski's result in the geometry of numbers.

With addition of remarks and comments and with references in the bibliography, the author stimulates readers to explore the subject beyond the scope of this book.

Reading information

Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.