Commutative Noetherian and Krull Rings

The aim of the book is to present fundamental concepts and results of commutative ring theory. It discusses both algebraic-geometrical and number-theoretical sources of commutative ring theory. A geometrical interpretation of numerous algebraical concepts is given (prime ideal, primary decomposition, local ring etc.), showing the inspiring role of algebraic geometry, but acquaintance with it is not assumed. Thus the book promotes the understanding of the importance of algebraic concepts and stimulates interest in algebraic geometry. Dedekind and Krull domains, normal domains, valuations serve as illustrations of number-theoretical aspects of the theory.

To read the book only the standard two semester algebra course is needed. Most of the sections end with exercises.