Commutative Ring Theory

Hideyuki Matsumura

Translated by M. Reid

In addition to being a beautiful and deep theory in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytic geometry. Let us start with a historical survey of its development. The most basic commutative rings are the ring Z of rational integers, and the polynomial rings over a field. Z is a principal ideal ring, and so is too simple to be ring-theoretically very interesting, but it was in the course of studying its extensions, the rings of integers of algebraic number fields, that Dedekind first introduced the notion of an ideal in the 1870s. For it was realized that only when prime ideals are used in place of prime numbers do we obtain the natural generalization of the number theory of Z.

جهت استعلام قيمت و سفارش چاپ اين محصول لطفا با انتشارات گنج حضور تماس حاصل فرماييد.