On the Mulitplicity of Zeros of Polynomials over Arbitrary Finite Dimensional K-Algebras.
On the multiplicity of .
On the Number of Faces of Simplicial Complexes and the Purity of Frobenius.
On the partial Euler-Poincare characteristics of certain systems of parameters in local rings.
On the Poincaré series for a plane divisorial valuation.
On the Prime Ideal of an Ordering of Higher Level.
On the singularities of Polar curves.
On the structure of nilpotent endomorphisms and applications.
On the structure of Noetherian symbolic Rees Algebras.
On the structure of non-excellent curve singularities in characteristic
On the structure of the canonical model of the Rees algebra and the associated graded ring of an ideal.
In this note we give a description of a morphism related to the structure of the canonical model of the Rees algebra R(I) of an ideal I in a local ring. As an application we obtain Ikeda's criteria for the Gorensteinness of R(I) and a result of Herzog-Simis-Vasconcelos characterizing when the canonical module of R(I) has the expected form.
On the Transitvity of regular differential Forms.
On the type sequences of some one dimensional rings.
On the upper semicontinuity intersection defect.
On the vanishing of local cohomology modules.
On torsion Gorenstein injective modules
In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if is a Gorenstein integral domain and is a left -module, then the torsion submodule of Gorenstein injective envelope of is also Gorenstein injective. We can also show that if is a torsion -module of a Gorenstein injective integral domain , then the Gorenstein injective envelope of is torsion.
On two-dimensional regular local rings and a lifting problem
One-Dimensional Local Rings with Reduced Associated Graded Ring and Their Hilbert Functions.
One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal
Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic...
Orderings of Higher Level and Semilocal Rings.