A left R-module Q is injective iff every R-homomorphism from a left ideal a ⊆ R to Q extends to a homomorphism R → Q. Baer 1940. Immediate consequence over a PID: injective modules are divisible. Provides a practical test: Q/Z is…
A left R-module Q is injective iff every R-homomorphism from a left ideal a ⊆ R to Q extends to a homomorphism R → Q. Baer 1940. Immediate consequence over a PID: injective modules are divisible. Provides a practical test: Q/Z is…