A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
A new Kurosh-Amitsur radical theory for proper semifields. II.
A new Kurosh-Amitsur radical theory for proper semifields. I.
A non-archimedean “curve integral” and its application to the construction of potentials and solutions of differential equations
A note on a connection between the Poincaré-Arnold-Melnikov integral and the Picard-Vessiot theory
We obtain an algebraic interpretation by means of the Picard-Vessiot theory of a result by Ziglin about the self-intersection of complex separatrices of time-periodically perturbed one-degree of freedom complex analytical Hamiltonian systems.
A note on a theorem of C. L. Siegel concerning Bessel's equation
A note on Abhyankar-Moh's approximate roots of polynomials.
A note on Babylonian square-root algorithm and related variants.
A note on characterizations of rings of constants with respect to derivations
Let A be a commutative algebra without zero divisors over a field k. If A is finitely generated over k, then there exist well known characterizations of all k-subalgebras of A which are rings of constants with respect to k-derivations of A. We show that these characterizations are not valid in the case when the algebra A is not finitely generated over k.
A note on differentially algebraic solutions of first order linear difference equations.
A note on finitely generated ideal-simple commutative semirings
Many infinite finitely generated ideal-simple commutative semirings are additively idempotent. It is not clear whether this is true in general. However, to solve the problem, one can restrict oneself only to parasemifields.
A note on Frobenius divided modules in mixed characteristics
If is a smooth scheme over a perfect field of characteristic , and if is the sheaf of differential operators on [7], it is well known that giving an action of on an -module is equivalent to giving an infinite sequence of -modules descending via the iterates of the Frobenius endomorphism of [5]. We show that this result can be generalized to any infinitesimal deformation of a smooth morphism in characteristic , endowed with Frobenius liftings. We also show that it extends to adic...
A note on functional equations of the -adic polylogarithms
A note on involutory automorphisms of and the use of algebraically independent numbers for the construction of diagonable matrices
A note on linear preserves of ternary cubic forms
A note on minimal Galois embeddings of abelian surfaces
A note on Robinson's non-negativity criterion
A note on the Hasse principle. Addenda
A Note on the Normality of Unramified, Abelian Extensions of Quadratic Extensions.
A note on the pp conjecture for sheaves of spaces of orderings
In this note we provide a direct and simple proof of a result previously obtained by Astier stating that the class of spaces of orderings for which the pp conjecture holds true is closed under sheaves over Boolean spaces.