Maximal Ideal in Simple Ring: Understanding the Relationship Between N and R/N

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Homework Statement


how that N is a maximal ideal in a ring R if and only if R/N is a simple ring. that is it is nontrivial and has no proper nontrivial ideals.


Homework Equations





The Attempt at a Solution


I don't know how to start. Please help.
 
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Hint: if you have an ideal in R/N, what do you get by taking its inverse image under the quotient map?
 
it is R?
 

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...
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