Completion of the process is familiar:
We can embed the original domain to the domain after Completion, we have to examine changes in valuation of:
Ostrowski Theorem tells us that the complete domain under archimedean valuation is certain:
The conclusion is amazing, we focus to resolve its proof to prove that the use of reductio ad absurdum, the key to prove that the problem into a number of instructions on K necessarily satisfy a quadratic equation on R:
We first explain the real number field contained in R:
So we emphasis on the nonarchimedan valuation,
The following two theorems but a p-adic promotion of:
In the field of rational function on valuation prime ideal for complete power series of the form field is obtained:
Secondly, with a projected limit can also be used in the theory of general valuation theory:
The key to remember is open neighborhood bases 0 element of two parts.
We valuation induction into the domain of algebraic extension of the above to:
We focus on analytical proof of this theorem:
First, the case is not difficult to discuss the Archimedean and make a limited number of expansion:
