On the product of a module by an ideal
On the Regularity of Graded k-Algebras of Krull Dimension ...1.
On the ring of quotients of a noetherian commutative ring with respect to the Dickson topology
On the ring of the variety of algebras over a ring
On the Structure of a Certain Class of Locally Compact Rings.
On the structure of certain normal ideals
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 nilpotent endomorphisms and applications.
On the structure of sequentially Cohen-Macaulay bigraded modules
Let be a field and be the standard bigraded polynomial ring over . In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” -modules with respect to . Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to are considered.
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 symmetric algebra of certain first syzygy modules
Let be a standard graded -algebra over a field . Then can be written as , where is a graded ideal of a polynomial ring . Assume that and is a strongly stable monomial ideal. We study the symmetric algebra of the first syzygy module of . When the minimal generators of are all of degree 2, the dimension of is calculated and a lower bound for its depth is obtained. Under suitable conditions, this lower bound is reached.
On the trivialization of line bundles over schemes
On the upper semicontinuity intersection defect.
On torsion free distributive 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 traces of exterior powers of a sum of two endomorphisms of a projective module
On Two Conjectures About Polynomial Rings.
Orientations and multiplicative structures of resolutions.