Einige Eigenschaften der Parameterideale und ihre Anwendungen für Buchsbaum Ringe
Let (R,m) be a Noetherian local ring and let I C R be an ideal. This paper studies the question of when m I is integrally closed. Particular attention is focused on the case R is a regular local ring and I is a reduced ideal. This question arose through a question posed by Eisenbud and Mazur on the existence of evolutions.
We describe all Kadison algebras of the form , where k is an algebraically closed field and S is a multiplicative subset of k[t]. We also describe all Kadison algebras of the form k[t]/I, where k is a field of characteristic zero.
The purpose of this paper is to define a new numerical invariant of valuations centered in a regular two-dimensional regular local ring. For this, we define a sequence of non-negative rational numbers δν = {δν(j)}j ≥ 0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation ν. This sequence is characterized by seven combinatorial properties, so that any sequence of non-negative rational numbers having the above properties...