On the minimal reduction and multiplicity of .
On the multiplicity of .
On the notions of characteristics and type for modules and their applications
On the number of generators of modules over Laurent Rings.
On the number of generators of modules over polynomial affine rings.
On the Poincaré series associated to the p-adic points on a curve
On the Polynomial Ring over a Mori Domain
On the Pythagoras number of a real irreducible algebroid curve.
On the reduction of Kronecker's modular systems whose elements are functions of two and three variables.
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 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 torsion free cover of the -module k
On the ultrametric Stone-Weierstrass theorem and Mahler's expansion
We describe an ultrametric version of the Stone-Weierstrass theorem, without any assumption on the residue field. If is a subset of a rank-one valuation domain , we show that the ring of polynomial functions is dense in the ring of continuous functions from to if and only if the topological closure of in the completion of is compact. We then show how to expand continuous functions in sums of polynomials.
On Two Conjectures About Polynomial Rings.
On unimodular complements
On unique and almost unique factorization of complete ideals II.