On the Pythagoras number of a real irreducible algebroid curve.
On the Radius and the Relation Between the Total Graph of a Commutative Ring and Its Extensions
On the reduction of Kronecker's modular systems whose elements are functions of two and three variables.
On the regularity and defect sequence of monomial and binomial ideals
When is a polynomial ring or more generally a standard graded algebra over a field , with homogeneous maximal ideal , it is known that for an ideal of , the regularity of powers of becomes eventually a linear function, i.e., for and some integers , . This motivates writing for every . The sequence , called the defect sequence of the ideal , is the subject of much research and its nature is still widely unexplored. We know that is eventually constant. In this article, after...
On the Regularity of Graded k-Algebras of Krull Dimension ...1.
On the ring of constants for derivations of power series rings in two variables
Let k[[x,y]] be the formal power series ring in two variables over a field k of characteristic zero and let d be a nonzero derivation of k[[x,y]]. We prove that if Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].
On the ring of invariants of F*2n.
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 rings of formal solutions of polynomial differential equations
The paper establishes the basic algebraic theory for the Gevrey rings. We prove the Hensel lemma, the Artin approximation theorem and the Weierstrass-Hironaka division theorem for them. We introduce a family of norms and we look at them as a family of analytic functions defined on some semialgebraic sets. This allows us to study the analytic and algebraic properties of this rings.
On the S-Euclidean minimum of an ideal class
We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from...
On the singularities of Polar curves.
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 Steenrod operations in cyclic cohomology.
On the structure and arithmetic of finitely primary monoids
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.