Ein Cohen-Macaulay-Kriterium mit Anwendungen auf den Konormalenmodul und den Differentialmodul.
Eine Bemerkung zum Kardinalprodukt
Equations for the set of overrings of normal rings and related ring extensions
We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.
Erweiterungen eines Ringes durch eine direkte Summe zyklischer Ringe.
Etale covers, bimodules and differential operators.
Extension of semiclean rings
This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.
Extensions factorielles
Factorial extensions of regular local rings and invariants of finite groups.
Factorisation de Ritt pour les polynômes exponentiels formels
Factorisations de morphismes d'anneaux commutatifs
Failure of splitting from module-finite extension rings.
Fast invertierbare Primideale der kommutativen Ringe.
Fermeture intégrale et changement de base
Fiber cones and the integral closure of ideals.
Let (R,m) be a Noetherian local ring and let I C R be an ideal. This paper studies the question of when m I is integrally closed. Particular attention is focused on the case R is a regular local ring and I is a reduced ideal. This question arose through a question posed by Eisenbud and Mazur on the existence of evolutions.
Field Composites with a Bounded Purely Inseparable Factor.
Finite dimensional rings of quotients.
In this paper we characterize commutative rings with finite dimensional classical ring of quotients. To illustrate the diversity of behavior of these rings we examine the case of local rings and FPF rings. Our results extend earlier work on rings with zero-dimensional rings of quotients.
Finite Polynomial Orbits in Finitely Generated Domains.
Finite Separable Field Extensions With Prescribed Extensions of Valuations. II
Flatness testing over singular bases
We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...
Forms and mappings. I: Generalities