In this note we give an algebraic proof of “deformation quantization” by making use of the theory of Unital Gröbner bases over a valuation ring. MSC: 16Z05,13P10 In this note we give an algebraic proof of deformation quantization (c.f. [7]). We do this be developing in (Sec. 1) the theory of unital Gröbner bases over a valuation ring. We then in (Sec. 2) obtain, almost immediately, our desired ...

We give a de nition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp((t)), which works uniformly for all p and all nite eld extensions of these elds, and in many other Henselian valued elds as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modi cation of the language of Macintyre. Furthermore, we show the negative result th...

We recall that a ring R is called near pseudo-valuation ring if every minimal prime ideal is a strongly prime ideal. Let R be a commutative ring, σ an automorphism of R and δ a σderivation of R. We recall that a prime ideal P of R is δ-divided if it is comparable (under inclusion) to every σ-invariant and δ-invariant ideal I (i.e. σ(I) ⊆ I and δ(I) ⊆ I) of R. A ring R is called a δ-divided ring...

In this paper we study rank one discrete valuations of the field k((X1, . . . ,Xn)) whose center in k[X1, . . . ,Xn] is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field o...