Gabriel Picavet

activity

20152022

most citedSome more combinatorics results on Nagata extensions

10 citations · 10 across the 6 of their papers we have counts for

collaborators

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9 papers · 1 filter

math.AC2022

Computing the closure of a support

Gabriel Picavet, Martine Picavet-L'Hermitte

When $E$ is an $R$ -module over a commutative unital ring $R$ , the Zariski closure of its support is of the form $V (O (E))$ where $O (E)$ is a unique radical…

math.AC2021

Closures and co-closures attached to FCP ring extensions

Gabriel Picavet, Martine Picavet-L'Hermitte

The paper deals with ring extensions $R \subseteq S$ and the poset $[R, S]$ of their subextensions, with a special look at FCP extensions (extensions such that $[R, S]$ is Artinian an…

math.AC2021

Splitting ring extensions

Gabriel Picavet, Martine Picavet-L'Hermitte

The paper deals with ring extensions $R \subseteq S$ and their lattices $[R, S]$ of subextensions and is mainly devoted to FCP extensions (extensions whose lattices are Artinian and…

math.AC2019

Catenarian FCP ring extensions

Gabriel Picavet, Martine Picavet-L'Hermitte

If $R \subseteq S$ is a ring extension of commutative unital rings, the poset $[R, S]$ of $R$ -subalgebras of $S$ is called catenarian if it verifies the Jordan-Hölder property. This…

math.AC2019

The Loewy series of an FCP (distributive) ring extension

Gabriel Picavet, Martine Picavet-L'Hermitte

We examine the Loewy series associated to the lattice of subalgebras of an extension of commutative rings.

math.AC2019

Boolean FIP ring extensions

Gabriel Picavet, Martine Picavet-L'Hermitte

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 latt…