In $\mathbb R$ and $\mathbb C$ with their usual smooth manifold structure, addition, multiplication and divisions by a non-zero element are all smooth functions. Are there other fields along with a non-$0$-dimensional smooth manifold structure in their underlying set satisfying this?
2026-03-25 14:30:47.1774449047
Are there "lie fields" other than $\mathbb R$ and $\mathbb C$?
78 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 SMOOTH-MANIFOLDS
- Smooth Principal Bundle from continuous transition functions?
- Possible condition on locally Euclidean subsets of Euclidean space to be embedded submanifold
- "Defining a smooth structure on a topological manifold with boundary"
- Hyperboloid is a manifold
- The graph of a smooth map is a manifold
- A finite group G acts freely on a simply connected manifold M
- An elementary proof that low rank maps cannot be open
- What does it mean by standard coordinates on $R^n$
- Partial Differential Equation using theory of manifolds
- Showing that a diffeomorphism preserves the boundary
Related Questions in TOPOLOGICAL-RINGS
- Extension of continuous map on group ring to a map on the complete group algebra
- $R$ be Noetherian ring. Let $I \subseteq J$ be proper ideals of $R$. If $R$ is $J$-adically complete, then is $R$ complete $I$-adically?
- $I$ be a finitely generated ideal of $R$ such that $R/I$ is a Noetherian and $R$ is $I$-adically complete. Then $R$ is Noetherian
- $R$ is Noetherian semilocal. $J:=\operatorname{Jac}(R)$. If $R/\operatorname{nil}(R)$ is $J$-adically complete, then $R$ is $J$-adically complete
- $\mathbb{Z}_p[\mathbb{Z}/p^{n}\mathbb{Z}]\cong \mathbb{Z}_p[T]/\left((T+1)^{p^n}-1\right)$ as topological rings?
- Is $\mathbb R$ with usual euclidean topology, homeomorphic with some topological field of positive characteristic?
- Could we define injective modules or projective modules for topological modules?
- Making the subgroup of units of a topological ring a topological group
- What's in a Noetherian $\mathbb{A}$-Module Ephemeralization?
- Is the ring $R$ a topological ring with respect to the following topology?
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?