Are there non-Archimedean fields without associated valuation or being a non-archimedan field implies it is a valuation field? I understand that a non-Archimedean field is a field which does not satisfy the Archimedean property.
2026-03-27 04:15:00.1774584900
Non-Archimedean Fields
3.2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in FIELD-THEORY
- Square classes of a real closed field
- Question about existence of Galois extension
- Proving addition is associative in $\mathbb{R}$
- Two minor questions about a transcendental number over $\Bbb Q$
- Is it possible for an infinite field that does not contain a subfield isomorphic to $\Bbb Q$?
- Proving that the fraction field of a $k[x,y]/(f)$ is isomorphic to $k(t)$
- Finding a generator of GF(16)*
- Operator notation for arbitrary fields
- Studying the $F[x]/\langle p(x)\rangle$ when $p(x)$ is any degree.
- Proof of normal basis theorem for finite fields
Related Questions in VALUATION-THEORY
- Does every valuation ring arise out of a valuation?
- Calculating the residue field of $\mathbb{F}_q(t)$ with respect to the valuation $-\deg$
- Different discrete valuation rings inside the same fraction field
- Extensions of maximally complete fields
- State Price Density Integration - Related to Ito's lemma
- Valuation on the field of rational functions
- Is every algebraically closed subfield of $\mathbb C[[X]]$ contained in $\mathbb C$?
- Working out an inequality in the proof of Ostrowski's Theorem
- The image of a valuation is dense in $\mathbb{R}$
- Kernel of the map $D^2+aD+b : k[[X]] \to k[[X]]$ , where $D :k[[X]] \to k[[X]]$ is the usual derivative map
Related Questions in ORDERED-FIELDS
- Embedding from Rational Numbers to Ordered Field is Order Preserving
- Ordered field with a maximum value
- Can algebraic numbers be compared using only rational arithmetic?
- Completeness of $\Bbb R(x)$?
- Does every ordered divisible abelian group admit an expansion (and how many) to an ordered field?
- Category theory and real closed fields
- Number of orbits of the natural action of order preserving bijections of $\mathbb Q$ on $\mathbb Q^n$
- well ordering principle and ordered field
- If $S<G:=\text{Gal}(E/R)$ is a Sylow 2-subgroup, then $[\text{Fix}_E(S):R] = [G:S]$
- Trouble constructing an ordered set that is not directed
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?