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, 𝔪), and we establish connections between the 𝔪-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 𝔪-adic completion, the completion in the ideal topology is not always Noetherian.
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