Proposition:
Proof:
Question: Why it's isomorphism?
2026-03-29 14:57:52.1774796272
Could you please explain the detail of the proof
57 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
Related 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 SELF-LEARNING
- Best book to study Lie group theory
- How do you prevent being lead astray when you're working on a problem that takes months/years?
- how to solve Lazy janitor problem
- How deep do you have to go before you can contribute to the research frontier
- Use the binomial theorem to prove that for $n$ a positive integer the following holds
- Am I right or wrong in this absolute value?
- good introduction to algebra over a field?
- What are the mathematical topics most essential for an applied mathematician?
- Are there any analysis textbooks like Charles Pinter's A book of abstract algebra?
- How to use the AOPS books?
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?
Define a homomorphism $f: S^{-1} A \rightarrow \bar{S}^{-1} (A/p)$ by sending $a/s$ to $\bar{a}/\bar{s}$ where $\bar{a}$ denotes the class of $a$ modulo $p$. Then show that this homomorphism is surjective and that its kernel is precisely $S^{-1} p$.