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arXiv · 1902.03946

Boolean FIP ring extensions

Gabriel Picavet·Martine Picavet-L'Hermitte
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Abstract

We characterize extensions of commutative rings $R \subseteq S$ whose sets of subextensions $[R,S]$ are finite ({\it i.e.} $R\subseteq S$ has the FIP property) and are Boolean lattices, that we call Boolean FIP extensions. Some characterizations involve ``factorial" properties of the poset $[R,S]$. A non trivial result is that each subextension of a Boolean FIP extension is simple (i.e. $R \subseteq S$ is a simple pair).

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Gabriel Picavet, Martine Picavet-L'Hermitte. 2019-02-11. Boolean FIP ring extensions. https://arxiv.org/abs/1902.03946

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