On the hereditary -Buchsbaum property for ideals and .
On the integral closure of ideals.
On the intersection graphs of ideals of direct product of rings
In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings.
On the intersection of invariant rings.
On the invariant theory of the Bézoutiant.
On the Jacobian ideal of the binary discriminant.
Let Δ denote the discriminant of the generic binary d-ic. We show that for d ≥ 3, the Jacobian ideal of Δ is perfect of height 2. Moreover we describe its SL2-equivariant minimal resolution and the associated differential equations satisfied by Δ. A similar result is proved for the resultant of two forms of orders d, e whenever d ≥ e-1. If Φn denotes the locus of binary forms with total root multiplicity ≥ d-n, then we show that the ideal of Φn is also perfect, and we construct a covariant which...
On the Jung method in positive characteristic
Let be a germ of normal surface with local ring covering a germ of regular surface with local ring of characteristic . Given an extension of valuation rings birationally dominating , we study the existence of a new such pair of local rings birationally dominating , such that is regular and has only toric singularities. This is achieved when is defectless or when is equal to
On the local uniformization problem
In this paper we give a short introduction to the local uniformization problem. This follows a similar line as the one presented by the second author in his talk at ALANT 3. We also discuss our paper on the reduction of local uniformization to the rank one case. In that paper, we prove that in order to obtain local uniformization for valuations centered at objects of a subcategory of the category of noetherian integral domains, it is enough to prove it for rank one valuations centered at objects...
On the maximal spectrum of commutative semiprimitive rings
The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).
On the multiplicity of .
On the number of compatibly Frobenius split subvarieties, prime -ideals, and log canonical centers
Let be a projective Frobenius split variety with a fixed Frobenius splitting . In this paper we give a sharp uniform bound on the number of subvarieties of which are compatibly Frobenius split with . Similarly, we give a bound on the number of prime -ideals of an -finite -pure local ring. Finally, we also give a bound on the number of log canonical centers of a log canonical pair. This final variant extends a special case of a result of Helmke.
On the Poincaré series for a plane divisorial valuation.
On the Prime Ideal of an Ordering of Higher Level.
On the product of a module by an ideal
On the Radius and the Relation Between the Total Graph of a Commutative Ring and Its Extensions
On the Regularity of Graded k-Algebras of Krull Dimension ...1.
On the stable equivalence problem for k[x,y]
L. Makar-Limanov, P. van Rossum, V. Shpilrain and J.-T. Yu solved the stable equivalence problem for the polynomial ring k[x,y] when k is a field of characteristic 0. In this note we give an affirmative solution for an arbitrary field k.
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
On the structure of Noetherian symbolic Rees Algebras.