Sentence examples for valuation field from inspiring English sources

We are given a complete discrete valuation field K of valuation ring O = O K and of perfect residue field k = O / π O.

One may note that | n | ≤ 1 in each valuation field, every triangle is isosceles and there may be no unit vector in a non-Archimedean normed space; cf. [12].

We present some new results for Artin Schreier extensions of arbitrary valuation fields in positive characteristic $p$.

Ultrametric spaces arise in the study of non-Archimedean analysis, and in particular in the study of Banach space over non-Archimedean valuation fields (see [4]).

Analysts at TCV and other experts in the real estate valuations field are researching the situation there hoping to identify the precise cause of Colorado's appraiser scarcity.

The shrinking supply of skilled real estate appraisers and barely a trickle in the pipeline of new apprentices entering the field presents an opportunity for recent college graduates and anyone with the requisite analytical, organizational and self-starter abilities necessary to succeed in the valuations field.

These asymmetrical structural relationships have important implications for the design and validity of monetary valuations and field auction experiments involving measurement of real payments for food product attributes.

If every element of K carries a valuation, then a field K is called a valued field; for convenience, we simply call it a field.

If the triangle inequality is replaced by | r + s | ≤ max { | r |, | s | } for all r, s ∈ K, then the function | ⋅ | is called a non-Archimedean valuation and the field is called a non-Archimedean field.

If the triangle inequality is replaced by r + s ≤ max { r, s }, ∀ r, s ∈ K, then the function | · | is called a non-Archimedean valuation, and the field is called a non-Archimedean field.

Let v be a valuation of a field K with a value group G v and a residue field k v, w be an extension of v to K ( x ).