## prove (n)⊇(m)⟺n∣m (n) \supseteq (m)\iff n\mid m\ (contains = divides for principal ideals)

For non-zero integers m and n, prove (m)⊂(n) iif n divides m, where (n) is the principal ideal. My attempt is following. For non-zero integers m and n, assume that (m)⊂(n). Then, mk∈(m) is also in (n). This means that ∃nh such that mk=nh. Then, we have m=nhk−1. Assume that n divides m for non-zero … Read more