Considering the following excerpt from page 98-99 of Hindry's Arithmetics.
Why does it follow from the exact sequence that $\text{N}(IJ) = \text{N}(J)\text{card}(J/IJ)$? Thanks in advance.
2025-01-12 19:18:47.1736709527
Page 99 of Hindry's Arithmetics, follows from exact sequence that $\text{N}(IJ) = \text{N}(J)\text{card}(J/IJ)$?
84 Views Asked by user245006 https://math.techqa.club/user/user245006/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Projective Indecomposable modules of quiver algebra
- Binary relations for Cobb-Douglas
- Relations among these polynomials
- Number of necklaces of 16 beads with 8 red beads, 4 green beads and 4 yellow beads
- Page 99 of Hindry's Arithmetics, follows from exact sequence that $\text{N}(IJ) = \text{N}(J)\text{card}(J/IJ)$?
- How to write the identity permutation as a product of transpositions
- Is $H$ a subgroup?
- $x=(0,\overline{1})$ and $y=(0,\overline{2})$ generate the same ideal in $R=\mathbb{Z}\times\mathbb{Z}/5\mathbb{Z}$
- Having some problems with understanding conics and graphing (eccentricity)
- Is this Cayley Diagram contradictory?
Related Questions in NUMBER-THEORY
- Page 99 of Hindry's Arithmetics, follows from exact sequence that $\text{N}(IJ) = \text{N}(J)\text{card}(J/IJ)$?
- How do I solve this over the integers
- How many ways to write a number $n$ as the product of natural numbers $\geq 2$?
- Representing integers as difference of semi-primes
- If $f,g$ are non-zero polynomials and $f$ divides $g$, then $\partial f \leq \partial g$.
- Conjugacy Class in Galois Representations
- Understanding Quadratic Residue Modulo n Structure
- Properties of the Gamma function
- Matrix of quadratic form (in Serre's general notion)?
- Find all pairs of positive integers $(n,k)$
Related Questions in ALGEBRAIC-NUMBER-THEORY
- Neukirch and a congruence condition.
- Page 99 of Hindry's Arithmetics, follows from exact sequence that $\text{N}(IJ) = \text{N}(J)\text{card}(J/IJ)$?
- Property of the norm of an ideal
- Application of GRR in number theory
- Conjugacy Class in Galois Representations
- Are there non-abelian totally real extensions?
- Polynomial rings which are Dedekind domains.
- How to construct an n-gon by ruler and compass?
- Ramification of prime ideal in Kummer extension
- Ideals of $\mathbb{Z}[i]$ geometrically
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- 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?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- 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
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity
In an exact sequence $$0\to A\to B\to C\to 0 $$of abelian groups we have $|B|=|A|\cdot |C|$.