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

[tinynerdi]

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.

 

[eok20]

Hint: if you have an ideal in R/N, what do you get by taking its inverse image under the quotient map?

 

[tinynerdi]

it is R?