A realization theorem for almost Dedekind domains

Balint Rago; Dario Spirito

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arXiv · 2405.04512

A realization theorem for almost Dedekind domains

Balint Rago·Dario Spirito

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Abstract

An integral domain $D$ is called an SP-domain if every ideal is a product of radical ideals. Such domains are always almost Dedekind domains, but not every almost Dedekind domain is an SP-domain. The SP-rank of $D$ provides a natural measure of the deviation of $D$ from being an SP-domain. In the present paper we show that every ordinal number $\alpha$ can be realized as the SP-rank of an almost Dedekind domain.

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Balint Rago, Dario Spirito. 2024-05-07. A realization theorem for almost Dedekind domains. https://arxiv.org/abs/2405.04512

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