# Math Help - Principal Ideals

1. ## Principal Ideals

How can I prove that every ideal of Zn is principal?

I've proved that if K is an ideal of Zn that contains an element k then it contains all the elements of the form mk (m in Zn)...But how can I prove that there are no elements that are not of the form mk?

THanks!

2. Originally Posted by WannaBe
How can I prove that every ideal of Zn is principal?

I've proved that if K is an ideal of Zn that contains an element k then it contains all the elements of the form mk (m in Zn)...But how can I prove that there are no elements that are not of the form mk?

THanks!
HINT: Look at what Euclid's algorithm tells you (that is, look at Bézout's identity).