The Ideal Completion of a Noetherian Local Domain

Abstract

The ideal topology on a integral domain R is the linear topology which has as a fundamental system of neighborhoods of 0 the nonzero ideals of R. We investigate the properties of the ideal topology on a Noetherian local domain R , and we establish connections between the -adic completion and the ideal completion. We give conditions under which the completion in the ideal topology is Noetherian, and we show that, unlike the -adic completion, the completion in the ideal topology is not always Noetherian.