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Fiber cones and the integral closure of ideals.

R. Hübl, C. Huneke (2001)

Collectanea Mathematica

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.

Local derivations for quotient and factor algebras of polynomials

Andrzej Nowicki, Ilona Nowosad (2003)

Colloquium Mathematicae

We describe all Kadison algebras of the form S - 1 k [ t ] , 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.

On proximity relations for valuations dominating a two-dimensional regular local ring.

José J. Aparicio, Angel Granja, Tomás Sánchez-Giralda (1999)

Revista Matemática Iberoamericana

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...

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