Algebraic extensions of the field of rational functions
β Scribed by Marvin Tretkoff
- Publisher
- John Wiley and Sons
- Year
- 1971
- Tongue
- English
- Weight
- 315 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0010-3640
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π SIMILAR VOLUMES
A function or a power series f is called differentially algebraic if it satisfies a Ε½ X Ε½ n. . differential equation of the form P x, y, y , . . . , y s 0, where P is a nontrivial polynomial. This notion is usually defined only over fields of characteristic zero and is not so significant over fields
Let M be a nonconstant polynomial in the polynomial ring R T =F q [T ] over the finite field F q . We show that the universal ordinary punctured distribution on 1 M R T ΓR T is a free abelian group and determine its rank. We also compute the torsion subgroups of the universal ordinary punctured even
It is well-known that functions uEWmlp(R) can be extended by a bounded linear operator E to functions EuC Wm7p(R"), if R is C"-regular and m s M . Here we prove a corresponding result for grid-functions with extension operators E, converging to E and mention some applications.
For a prime number p we characterize the finitely generated maximal pro-p Galois groups of algebraic extensions of Q. This generalizes a characterization by Jensen and Prestel of the maximal abelian quotients of these Galois groups. As an application we show that the Witt rings of the algebraic exte