On some class groups of an integral domain
On Strong Going-Between, Going-Down, And Their Universalizations, II
We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if are domains such that is an LFD universally going-down domain and is algebraic over , then the inclusion map satisfies GB for each . However, for any nonzero ring...
On the Complete Integral Closure of a Mori Domain
On the Dimension and Integrality of Symmetric Algebras.
On the local uniformization problem
In this paper we give a short introduction to the local uniformization problem. This follows a similar line as the one presented by the second author in his talk at ALANT 3. We also discuss our paper on the reduction of local uniformization to the rank one case. In that paper, we prove that in order to obtain local uniformization for valuations centered at objects of a subcategory of the category of noetherian integral domains, it is enough to prove it for rank one valuations centered at objects...
On the structure and arithmetic of finitely primary monoids
Openly embedding local noetherian domains.
Polynômes à valeurs entières ainsi que leurs dérivées
Polynomes à valeurs entières et propriété de Skolem.
Polynomial cycles in certain local domains
1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple of distinct elements of R is called a cycle of f if for i=0,1,...,k-2 and . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number , depending only on the degree N of K. In this note we consider...
Polynomial Cycles in Finitely Generated Domains.
Precobalanced and cobalanced sequences of modules over domains
The class of pure submodules () and torsion-free images () of finite direct sums of submodules of the quotient field of an integral domain were first investigated by M. C. R. Butler for the ring of integers (1965). In this case and short exact sequences of such modules are both prebalanced and precobalanced. This does not hold for integral domains in general. In this paper the notion of precobalanced sequences of modules is further investigated. It is shown that as in the case for abelian groups...
Proof of the combinatorial nullstellensatz over integral domains, in the spirit of Kouba.
Proprietá di ideali in domini d'integritá noetheriani
Propriété Ci revue et généralisée
Propriété d'approximation pour les éléments algébriques
Quotient Overrings
Remarks on Blowing-Up Divisorial Ideals.
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...
Rings and Partly Ordered Systems.