Recognizing cluster algebras of finite type.
Reconstructing birational maps from their face functions.
Regularity of Ideals and their Radicals.
Regularly weakly based modules over right perfect rings and Dedekind domains
A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains.
Relative multiplication and distributive modules
We study the construction of new multiplication modules relative to a torsion theory . As a consequence, -finitely generated modules over a Dedekind domain are completely determined. We relate the relative multiplication modules to the distributive ones.
Relèvements de schémas et algèbres de Monsky-Washnitzer : théorèmes d équivalence et de pleine fidélité II
Remarks and corrections to the paper "Principal ideal theorems for holomorphy rings in fields".
Remarks on iteration of formal automorphisms.
Remarks on the elementary theories of formal and convergent power series
Remarque sur les anneaux de fractions et la factorisation
Remarques sur la factorisation dans les anneaux commutatifs
Remarques sur les idéaux de polynômes et de formes différentielles extérieures I
Remarques sur les idéaux de polynômes et de formes différentielles extérieures II
Résidu de Grothendieck et forme de Chow.
We show an explicit relation between the Chow form and the Grothendieck residue; and we clarify the role that the residue can play in the intersection theory besides its role in the division problem.
Residues and effective Nullstellensatz.
Resolutions by mapping cones.
Résolvandes et espaces homogènes principaux de schémas en groupe
Resolving Algebras with Straightening Law
Ring extensions with some finiteness conditions on the set of intermediate rings
A ring extension is said to be FO if it has only finitely many intermediate rings. is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair...
Ringepimorphismen und Morita-projektive Moduln über kommutativen Dedekind-Ringen.