10 citations · 18 across the 13 of their papers we have counts for
15 papers
Quasi-maximal ideals and ring extensions
Gabriel Picavet, Martine Picavet-L'Hermitte
Alan and al. defined and studied quasi-maximal ideals. We add a comprehensive characterization of these ideals, introducing submaximal ideals. The conductor of a finite minimal ext…
Pairs of rings sharing their units
Gabriel Picavet, Martine Picavet L'Hermitte
We are working in the category of commutative unital rings and denote by the group of units of a nonzero ring . An extension of rings , satisfying $…
Computing the closure of a support
Gabriel Picavet, Martine Picavet-L'Hermitte
When is an -module over a commutative unital ring , the Zariski closure of its support is of the form where is a unique radical…
Distributive FCP extensions
Gabriel Picavet, Martine Picavet-L'Hermitte
We are dealing with extensions of commutative rings whose chains of the poset of their subextensions are finite ({\em i.e.} has the FCP proper…
Around Prufer extensions of rings
Gabriel Picavet, Martine Picavet-L'Hermitte
The paper intends to apply the properties of Prüfer extensions, investigated in the Knebusch-Zhang book, to ring extensions . The integral closure of $R…
Closures and co-closures attached to FCP ring extensions
Gabriel Picavet, Martine Picavet-L'Hermitte
The paper deals with ring extensions and the poset of their subextensions, with a special look at FCP extensions (extensions such that is Artinian an…