Let R be a ring. Let n > 0. Let M be an R-module generated by < n elements. Let f : R^{⊕ n} —> M be an R-module map. Then Ker(f) is nonzero. See Lemma Tag 05WI.

Slogan: R^{n + 1} —> R^n cannot be injective.

Let R be a ring. Let n > 0. Let M be an R-module generated by < n elements. Let f : R^{⊕ n} —> M be an R-module map. Then Ker(f) is nonzero. See Lemma Tag 05WI.

Slogan: R^{n + 1} —> R^n cannot be injective.