Definition 10.120.14 (034W)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.120: Factorization
Definition 10.120.14 (cite)

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Definition 10.120.14. A Dedekind domain is a domain $R$ such that every nonzero ideal $I \subset R$ can be written as a product

$I = \mathfrak p_1 \ldots \mathfrak p_ r$

of nonzero prime ideals uniquely up to permutation of the $\mathfrak p_ i$ .

Comments (1)

Comment #8128 by Aise Johan de Jong on February 22, 2023 at 19:51

Here the empty product (the case $r = 0$ ) gives the ideal $I = R$ .

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