Commutative group rings of finite representation type

Finite Commutative Rings

‡ Every function on a finite residue class ring D/I of a Dedekind domain D is induced by an integer-valued polynomial on D that preserves congruences mod I if and only if I is a power of a prime ideal. If R is a finite commutative local ring with maximal ideal P of nilpotency N satisfying for all a, b∈R, if ab∈ P then a∈ P k , b∈ P j with k+ j ≥min(n,N), we determine the number of functions (as...

Representation of real commutative rings

During the last 10 years there have been several results on the representation of real polynomials, positive on some semi-algebraic subset of R. These results started with a solution of the moment problem by Schmüdgen for corresponding sets. Later Wörmann realized that the same results could be obtained by the so-called “Kadison-Dubois” Representation Theorem. The aim of our talk is to present ...

Commutative Rings and Finite Fields

Commutative Nil Clean Group Rings

In [5] and [6], a nil clean ring was defined as a ring for which every element is the sum of a nilpotent and an idempotent. In this short article we characterize nil clean commutative group rings.

Diophantine properties of finite commutative rings

Simple observations on diophantine definability over finite commutative rings lead to a characterization of those rings in terms of their diophantine behavior. A.M.S. Classification: 13M10, 11T06, 03G99.