Finitely-generated M over (R,m) local: mM = M ⟹ M = 0. Equiv: M/mM generates M via any lift. Workhorse of commutative algebra.
Finitely-generated M over (R,m) local: mM = M ⟹ M = 0. Equiv: M/mM generates M via any lift. Workhorse of commutative algebra.