I am a final year undergraduate student. I am doing my research on Non-Abelian Kummer Extensions. Can someone please introduce me to formal definition of Non-abelian Kummer Extensions. I know it is some type of Galois extension but I don't how to define it. Is it just a non abelian Galois extension or does non Abelian Galois extensions need some requirements to become non Abelian Kummer Extensions. Please help me in this regard. I am following the book "Algebra" by Serge Lang. Can someone refer me some other literature on this topic. Thank you!
2026-03-29 19:48:15.1774813695
Request for reference books, articles, papers on the topic topic of Non Abelian Kummer Extensions.
45 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMMUTATIVE-ALGEBRA
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- Extending a linear action to monomials of higher degree
- Tensor product commutes with infinite products
- Example of simple modules
- Describe explicitly a minimal free resolution
- Ideals of $k[[x,y]]$
- $k[[x,y]]/I$ is a Gorenstein ring implies that $I$ is generated by 2 elements
- There is no ring map $\mathbb C[x] \to \mathbb C[x]$ swapping the prime ideals $(x-1)$ and $(x)$
- Inclusions in tensor products
- Principal Ideal Ring which is not Integral
Related Questions in NONCOMMUTATIVE-ALGEBRA
- If $P$ is a prime ideal of $R[x;\delta]$ such as $P\cap R=\{0\}$, is $P(Q[x;\delta])$ also prime?
- In a left noetherian ring, does having a left inverse for an element guarantee the existence of right inverse for that element?
- Are there rational coefficients that hold such properties?
- A characterization for minimal left ideals of semisimple rings
- $A \subseteq B \subseteq C$, with $A$ and $C$ simple rings, but $B$ is not a simple ring
- Simplicity of Noetherian $B$, $A \subseteq B\subseteq C$, where $A$ and $C$ are simple Noetherian domains
- Completion of localization equals the completion
- Representations of an algebra
- A characterization of semisimple module related to anihilators
- Counterexample request: a surjective endomorphism of a finite module which is not injective
Related Questions in GALOIS-EXTENSIONS
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Non-galois real extensions of $\mathbb Q$
- How is $\operatorname{Gal}(K^{nr}/K)$ isomorphic to $\operatorname{Gal}(\bar{k}/k)$?
- Corollary of Proposition 11 in Lang's Algebraic Number Theory
- The automorphisms of the extension $\mathbb{Q}(\sqrt[4]{2})/\mathbb{Q}$.
- First cohomology group of the $n$-torsion of an elliptic curve
- Given a Galois extension with $Gal_F(E) \simeq S_3$, is $E$ a splitting field of an irreducible cubic polynomial over F?
- Polynomial coefficients from GF(2^k) to GF(2)
- $\mathbb{Q}(t+t^{-1}) \subseteq \mathbb{Q}(t)$, where $t$ is a variable
- Is the integral closure of a ring of integers in finite separable extension a ring of integers?
Related Questions in CLASS-FIELD-THEORY
- $(K^*)$ in $K^*$
- Surjectivity of the inv map in Global class field theory
- On the Galois group of the maximal $p$-abelian $p$-ramified extension of a number field
- Which primes are ramified?
- Computing Hilbert Class Field of a number field
- Existence of totally real number fields of any degree
- How is the Artin map defined for ramified extensions?
- Brauer group of global fields
- Adeles under base change
- What is the structure of the $H$?
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?