Injective algebra

Summary

An algebra in a class of algebras is injective when every homomorphism into it from a subalgebra extends to the whole algebra. It is the universal-algebra form of an injective object, with embeddings in the role of monomorphisms. In the variety of abelian groups the injective algebras are the divisible groups, and in modules they are the injective modules. Injective algebras and injective hulls are tools for embedding algebras into well-behaved ones.