… N* (A, T, fAT), we introduce a field K of characteristic zero which contains the p'-th roots of
unity, and we choose a nontrivial … Notice that the a'-th iterate of of a is a completely continuous …

… We state and prove a generalization of Ax’s theorem on the transcendence degree of
solutions of the differential equation of the exponential map. We also discuss a positive …

… Theorem 4 in [A] a general transcendence theorem … a few additions, a portion of Ax's general
discussion of the module of differentials. Let A be a commutative ring and B a commutative A…

… Let 5(#i, a2) be a distance function in A and let e>0 be given. Since A is compact there is a
X(e) >0 … The theorem will follow when we have proved that A is a deformation retract10 of T. …

… This paper is about a theorem and the pictures that go with it. The … The first step is to see
Ax as a combination of the columns of A. Until then the multiplication Ax is just numbers. This …

… shall now show that cij is its multiple and as a result (6) is again valid in F[x]. Let g be any
factor irreducible in F[x] which is common to a,, and b#, then the invariant factors of A and B are …

… The simplest proof of the Ax–Katz theorem and its extension to character sums were given
in [14]. A reduction of the Ax–Katz theorem for a system of equations to Ax’s theorem for a …

… note we present a new simple proof of Kuttner's theorem. However, the main purpose of the
note … The object is to prove a general theorem on matrix transformations which is of some …

… And if Ax is a fundamental root of A22, we have again \XX\ ^A^^^A^, … 6 from our Theorem
I. On the other hand, for an irreducible matrix A, if we have | Ax| = | A \n and for a k with 2 ^ k < n …

… A typical example of a valued field is Qp, naturally equipped with the p-adic valuation vp. A
valuation on a field encompasses a … Note that the value group sort is a little more than a group …