In [1] Briançon and Skoda proved, using analytic methods, that if I is an ideal in the convergent power series ring C{x1, . . . , xn} then In, the integral closure of I, is contained in I. Extensive… (More)

It is proved that whenever P is a prime ideal in a commutative Noethe-rian ring such that the P-adic and the P-symbolic topologies are equivalent, then the two topologies are equivalent linearly.… (More)

We study applications of discrete valuations to ideals in analytically irreducible domains, in particular applications to zero divisors modulo powers of ideals. We prove a uniform version of Izumi's… (More)

We explicitly calculate the normal cones of all monomial primes which define the curves of the form (tL, tL+1, . . . , tL+n), where n ≤ 4. All of these normal cones are reduced and Cohen-Macaulay,… (More)

The regularity part follows from the primary decompositions part, so the heart of this paper is the analysis of the primary decompositions. In [S], this was proved for the primary components of… (More)

Swanson was partially motivated by the analogous question for “Frobenius powers”, which has important applications to the theory of tight closure (the so-called “localization problem;” see [HH,… (More)

We start with any polynomial p(x, y) defining a plane curve with singularity at 0 ∈ C. Let π: C̃ → C denote the blow-up of C at the origin and let j be a positive integer. The data (j, p) determines… (More)

Let R be a Noetherian ring and I an ideal in R. Then there exists an integer k such that for all n 1 there exists a primary decomposition I n = q 1 \ \ q s such that for all i, p q i nk q i. Also,… (More)

Leonard and Pellikaan [2003] devised an algorithm for computing the integral closure of weighted rings that are finitely generated over finite fields. Previous algorithms proceed by building… (More)