Definition:Monomorphism (Abstract Algebra)

A monomorphism is a homomorphism which is an injection.

Group Monomorphism
If both $$\left({G, \circ}\right)$$ and $$\left({H, *}\right)$$ are groups, then a monomorphism $$\phi: \left({G, \circ}\right) \to \left({H, *}\right)$$ is called a group monomorphism.

Ring Monomorphism
If both $$\left({R, +, \circ}\right)$$ and $$\left({S, +, *}\right)$$ are rings, then a monomorphism $$\phi: \left({R, +, \circ}\right) \to \left({S, +, *}\right)$$ is called a ring monomorphism.