A Bertini type theorem in analytic geometry.
A completion of is a field
We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields . Further, we show that is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.
A Counterexample to Artin Approximation With Respect to Subrings.
A generalization of formal schemes and rigid analytic varieties.
A model-theoretic transfer theorem for henselian valued fields.
A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
A note on quasi-complete local rings
A note on the countable union of prime submodules.
A Note on the Hochschild Homology and Cyclic Homology of a topological Algebra.
A proof of Pisot's th root conjecture.
A property of non excellent rings.
A Remark on Two-Dimensional Local Rings with the Property of Approximation.
A Theorem on Solutions of Analytic Equations with Applications to Deformations of Complex Structures.
Abelian extensions of an absolutely unramified local field with general residue field.
About Nagata Rings.
Adic-completion and some dual homological results.
Let a be an ideal of a commutative ring A. There is a kind of duality between the left derived functors Uia of the a-adic completion functor, called local homology functors, and the local cohomology functors Hai.Some dual results are obtained for these Uia, and also inequalities involving both local homology and local cohomology when the ring A is noetherian or more generally when the Ua and Ha-global dimensions of A are finite.
A-Endomorphismes de A(X).
Algebraic tubular neighbourhoods I.
Algèbres de Hadamard
An -algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem
Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.