On quasi-projective uniserial modules
On Rings admitting orderings and 2-primary chains of orderings of higher level.
On roots of polynomials with power series coefficients
We give a deepened version of a lemma of Gabrielov and then use it to prove the following fact: if h ∈ 𝕂[[X]] (𝕂 = ℝ or ℂ) is a root of a non-zero polynomial with convergent power series coefficients, then h is convergent.
On the algebraic compactness of some complete modules
On the approximation property of excellent rings.
On the Completion of a Valuation Ring.
On the Diophantine equation ... (X, Y) = ... (x, y).
On the Jacobian conjecture and the configurations of roots.
On the Jacobian criterion of formal smoothness.
We give a short proof of the Jacobian criterion of formal smoothness using the Lichtenbaum-Schlessinger cotangent complex.
On the Nonflatness of Analytic Tensor Product.
On the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields
We will prove that the Pierce-Birkhoff Conjecture holds for non-singular two-dimensional affine real algebraic varieties over real closed fields, i.e., if is such a variety, then every piecewise polynomial function on can be written as suprema of infima of polynomial functions on . More precisely, we will give a proof of the so-called Connectedness Conjecture for the coordinate rings of such varieties, which implies the Pierce-Birkhoff Conjecture.
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 Structure of a Certain Class of Locally Compact Rings.
On the structure of non-excellent curve singularities in characteristic
On the Weierstrass division.
On two-dimensional regular local rings and a lifting problem
On valuation spectra
Openly embedding local noetherian domains.
Ordered fields.