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...