Commutative Algebra/The lattice of submodules, Noether isomorphism theorems

Quotients

Exercises

• Let $m,n\in \mathbb {N}$. Prove that $(m\mathbb {Z} )/(n\mathbb {Z} )\cong \mathbb {Z} {\big /}{\frac {n}{\gcd(m,n)}}\mathbb {Z}$.