Proving Ideal of R/J is Contained in I of R Containing J

  • Thread starter Thread starter chibulls59
  • Start date Start date
chibulls59
Messages
8
Reaction score
0

Homework Statement


Suppose that J is an ideal of R, and consider the ring R/J = {r + J | r 2 R}.
Prove that X is an ideal of R/J is and only if there is an ideal I of R containing J such
that J c I c R.


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
What was your attempt at a solution?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Find the equation of the tangent plane and normal to a surface
Replies
1
Views
1K
I Definition of minimal ideal using symbolic logic notation
Replies
3
Views
567
Use greedy vertex coloring algorithm to prove the upper bound of χ
Replies
0
Views
51
Union of Prime Ideals Contains an Ideal
Replies
5
Views
2K
Order of element and order of cyclic group coincide
Replies
1
Views
2K
##R[x,y]## and ##R[y,x]## are Ring Isomorphic
Replies
3
Views
2K
Is There a Simple Way to Show GL(n,C) is a Lie Group?
Replies
4
Views
2K
What is the probability of getting r heads before s tails?
Replies
37
Views
6K
Proof of a vector identity in electromagnetism
Replies
9
Views
2K
Proving the Ideal Status of K in R: I and J as Ideals in a Ring R
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top