Simple Galois extensions of two-dimensional affine rational domains
Some cardinal invariants for valuation domains
Some epimorphic regular contexts.
Some Homological properties of commutative semitrivial ring extensions.
Some remarks on the altitude inequality
We introduce and study a new class of ring extensions based on a new formula involving the heights of their primes. We compare them with the classical altitude inequality and altitude formula, and we give another characterization of locally Jaffard domains, and domains satisfying absolutely the altitude inequality (resp., the altitude formula). Then we study the extensions R ⊆ S where R satisfies the corresponding condition with respect to S (Definition 3.1). This leads to a new characterization...
Star operations in extensions of integral domains
An extension of integral domains is strongly-compatible (resp., -compatible) if (resp., for every nonzero finitely generated fractional ideal of . We show that strongly -compatible implies -compatible and give examples to show that the converse does not hold. We also indicate situations where strong -compatibility and its variants show up naturally. In addition, we study integral domains such that is strongly -compatible (resp., -compatible) for every overring of .
Subintegrality, invertible modules and the Picard group
Submodules of secondary modules.
Sulla proprietà di estensione in anelli noetheriani
Sur les Extensions Triviales Commutatives
Nous caractérisons les extensions triviales semiGoldie, de cogénération finie, mininjectives et quasi-Frobeniusiens. Comme application, nous montrons que tout anneau noethérien s’injecte dans un anneau quasi-Frobeniusien.
Sur les suranneaux minimaux.