problem:

solution:Determine all ideals of Z/Z10.

The first paragraph is just saying the ideals generated by the units in the ring is the whole ring correct?

Also, the principal ideals generated by 2, 4 and 8 are all the same correct? So those are three ideals or just one?

So, in the final answer there are 4 ideals in total right?

And finally why do we care about Ideals so much? What use do they even have besides giving students of average intelligence a giant headache in intro abstract algebra course lol?