The Classification of Homogeneous Cohen-Macauly Rings of Finite Representation Type.
The Conductor of one-dimensional Gorenstein Rings in their blowing-up.
The cones associated to some tranversal polymatroids.
The Construction of a Module of Finite Projective Dimension from a Finitely Generated Module of Finite Injective Dimension.
The covariety of perfect numerical semigroups with fixed Frobenius number
Let be a numerical semigroup. We say that is an isolated gap of if A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by the multiplicity of a numerical semigroup . A covariety is a nonempty family of numerical semigroups that fulfills the following conditions: there exists the minimum of the intersection of two elements of is again an element of , and for all such that We prove that the set is a perfect numerical semigroup with...
The effect on associated prime ideals produced by an extension of the base field.
The equality in Buchsbaum rings
The equations of Rees algebras of ideals with linear presentation.
The Gorenstein Property Depends on Characteristic
The -vector of a Gorenstein toric ring of a compressed polytope.
The homological theory of maximal Cohen-Macaulay approximations
The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant
Given a real analytic vector field tangent to a hypersurface with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra associated with the singularity of the vector field on . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation of...
The Koszul Algebra of a Codimension 2 Embedding.
The Lazarsfeld-Rao problem for Buchsbaum curves
The second Brauer-Thrall conjecture for isolated singularities of excellent hypersurfaces.
The Structure of Certain Ideal Transforms.
Toward parametric Cohen-Macaulayfication of two-dimensional finite local cohomology domains.
Towards a theory of Bass numbers with application to Gorenstein algebras
The notion of Gorenstein rings in the commutative ring theory is generalized to that of Noetherian algebras which are not necessarily commutative. We faithfully follow in the steps of the commutative case: Gorenstein algebras will be defined using the notion of Cousin complexes developed by R. Y. Sharp [Sh1]. One of the goals of the present paper is the characterization of Gorenstein algebras in terms of Bass numbers. The commutative theory of Bass numbers turns out to carry over with no extra changes....
Traces in strict Frobenius algebras and strict complete intersections.
Two Notes on Flatness.