Groupes de Picard et problèmes de Skolem. I
Groupes de Picard et problèmes de Skolem. II
Ideal theory in Prüfer rings with zero divisors.
Ideal-theoretic characterizations of valuation and Prüfer monoids
It is well known that an integral domain is a valuation domain if and only if it possesses only one finitary ideal system (Lorenzen -system of finite character). We prove an analogous result for root-closed (cancellative) monoids and apply it to give several new characterizations of Prüfer (multiplication) monoids and integral domains.
Integer-valued polynomials on algebras: a survey
We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature.
Invarianten wesentlicher Überdeckungen.
Inverse zero-sum problems in finite Abelian p-groups
We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over...
Klassen von Moduln über Dedekind-Ringen und Satz von Stein-Serre
Kummer theory of abelian varieties and reductions of Mordell-Weil groups
Local D-Rings.
Manis valuations and Prüfer extensions
Manis valuations and Prüfer extensions. I.
Matroids over a ring
We introduce the notion of a matroid over a commutative ring , assigning to every subset of the ground set an -module according to some axioms. When is a field, we recover matroids. When , and when is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, i.e. tropical linear spaces, respectively. More generally, whenever is a Dedekind domain, we extend all the usual properties and operations holding for matroids (e.g., duality), and...
Maximal non-Jaffard subrings of a field.
A domain R is called a maximal non-Jaffard subring of a field L if R ⊂ L, R is not a Jaffard domain and each domain T such that R ⊂ T ⊆ L is Jaffard. We show that maximal non-Jaffard subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dimv R = dim R + 1. Further characterizations are given. Maximal non-universally catenarian subrings of their quotient fields are also studied. It is proved that this class of domains coincides with the previous class when R is integrally...
Mittag-Leffler modules and semi-hereditary rings
Modular quadratic and Hermetian forms over Dedekind rings. I.
Modular quadratic and Hermitian forms over Dedekind rings.
Morita-injektive Moduln über kommutativen Dedekind-Ringen.
Non commutative Krull domains.
Non-unique factorizations in orders of global fields.