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arXiv · 2207.07366

Radical semistar operations

Dario Spirito
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Abstract

We introduce and study the set of radical stable operations of an integral domain $D$. We show that their set is a complete lattice that is the join-completion of the set of spectral semistar operations, and we characterize when every radical operation is spectral (under the hypothesis that $D$ is rad-colon coherent). When $D$ is a Prüfer domain such that every set of minimal prime ideals is scattered, we completely classify stable semistar operations.

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Dario Spirito. 2022-07-15. Radical semistar operations. https://arxiv.org/abs/2207.07366

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