# Closures and co-closures attached to FCP ring extensions

@inproceedings{Picavet2021ClosuresAC, title={Closures and co-closures attached to FCP ring extensions}, author={Gabriel Picavet and Martine Picavet-L'Hermitte}, year={2021} }

The paper deals with ring extensions R ⊆ S and the poset [R,S] of their subextensions, with a special look at FCP extensions (extensions such that [R,S] is Artinian and Noetherian). When the extension has FCP, we show that there exists a co-integral closure, that is a least element R in [R,S] such that R ⊆ S is integral. Replacing the integral property by the integrally closed property, we are able to prove a similar result for an FCP extension. The radicial closure of R in S is well known. We… Expand

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