Resolutions by mapping cones.
Resolutions of generic points lying on a smooth quadric.
Résolvandes et espaces homogènes principaux de schémas en groupe
Resolving Algebras with Straightening Law
Restricted homological dimensions over local homomorphisms and Cohen-Macaulayness
We define and study restricted projective, injective and flat dimensions over local homomorphisms. Some known results are generalized. As applications, we show that (almost) Cohen-Macaulay rings can be characterized by restricted homological dimensions over local homomorphisms.
Résultats récents d'algèbre commutative effective
Résultats récents sur l'approximation des morphismes en algèbre commutative
Retracts that are kernels of locally nilpotent derivations
Let be a field of characteristic zero and a -domain. Let be a retract of being the kernel of a locally nilpotent derivation of . We show that if for some principal ideal (in particular, if is a UFD), then , i.e., is a polynomial algebra over in one variable. It is natural to ask that, if a retract of a -UFD is the kernel of two commuting locally nilpotent derivations of , then does it follow that ? We give a negative answer to this question. The interest in retracts comes...
Révêtements étales
Right Symbolic Powers and Classical Localization in Right Noetherian Rings.
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...
Ringe der Charakteristik p und Frobeniusfunktoren.
Ringe mit nur endlich vielen Isomorphieklassen von maximalen, unzerlegbaren Cohen-Macaulay-Moduln.
Ringepimorphismen und Morita-projektive Moduln über kommutativen Dedekind-Ringen.
Rings all of whose additive endomorphisms are left multiplications.
Rings and Partly Ordered Systems.
Rings generalized by tripotents and nilpotents
We present new characterizations of the rings for which every element is a sum of two tripotents and a nilpotent that commute. These extend the results of Z. L. Ying, M. T. Koşan, Y. Zhou (2016) and Y. Zhou (2018).
Rings in Which Pure Ideals are Generated by Idempotents.
Rings of constants of four-variable Lotka-Volterra systems
Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C 1, C 2, C 3, C 4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.
Rings of constants of generic 4D Lotka-Volterra systems
We show that the rings of constants of generic four-variable Lotka-Volterra derivations are finitely generated polynomial rings. We explicitly determine these rings, and we give a description of all polynomial first integrals of their corresponding systems of differential equations. Besides, we characterize cofactors of Darboux polynomials of arbitrary four-variable Lotka-Volterra systems. These cofactors are linear forms with coefficients in the set of nonnegative integers. Lotka-Volterra systems...