A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
A note on finitely generated commutative rings
A note on the computation of multiplicities.
Absolutely S-domains and pseudo-polynomial rings
A domain R is called an absolutely S-domain (for short, AS-domain) if each domain T such that R ⊆ T ⊆ qf(R) is an S-domain. We show that R is an AS-domain if and only if for each valuation overring V of R and each height one prime ideal q of V, the extension R/(q ∩ R) ⊆ V/q is algebraic. A Noetherian domain R is an AS-domain if and only if dim (R) ≤ 1. In Section 2, we study a class of R-subalgebras of R[X] which share many spectral properties with the polynomial ring R[X] and which we call pseudo-polynomial...
An Application of Jonsson Modules to Some Questions Concerning Proper Subrings.
Anneaux de Goldman
Anneaux presque intégralement clos
Anwendung von Ideal - Transformationen.
C-anneaux, E-anneaux et formule de la dimension
Carrés cartésiens et anneaux de pseudo-valuation
Carrés cartésiens et couples d'anneaux ayant les mêmes idéaux premiers
Classes of commutative rings characterized by going-up and going-down behavior
Commutative domains large in their -adic completions
Commutative rings whose principal ideals are annihilators
Conductive Integral Domains as Pullbacks.
Die Struktur flacher lokaler Erweiterungen lokaler Ringe
Dimension des couples d'anneaux partageant un idéal
Discrete valuation domains and ranks of their maximal extension
Diskriminanten und Picard-Invarianten freier quadratischer Erweiterungen.
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.