Dedekind rings

Abstract

A Dedekind ring R is defined as an integral domain which has the following three properties A. R is a Noetherian ring. B. Every prime ideal in R is a maximal ideal. C. R is integrally closed in its quotient field P. A Noetherian ring is a commutative ring for which the divisor chain condition is valid. If the divisor chain condition is valid in a ring r then every set of ideals A1 in R such that A1 C AI+1 properly, is a finite set. For Noetherian rings a theory of ideals may be developed. The main results of this theory are listed in the appendix [TRUNCATED]