Isomorphism Preserves Semigroups/Proof 2
Jump to navigation
Jump to search
Theorem
Let $\struct {S, \circ}$ and $\struct {T, *}$ be algebraic structures.
Let $\phi: S \to T$ be an isomorphism.
If $\struct {S, \circ}$ is a semigroup, then so is $\struct {T, *}$.
Proof
An isomorphism is an epimorphism.
The result follows as a direct corollary of Epimorphism Preserves Semigroups.
$\blacksquare$