Definition:Semigroup Epimorphism
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Definition
Let $\left({S, \circ}\right)$ and $\left({T, *}\right)$ be semigroups.
Let $\phi: S \to T$ be a (semigroup) homomorphism.
Then $\phi$ is a semigroup epimorphism if and only if $\phi$ is a surjection.
Linguistic Note
The word epimorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix epi- meaning onto.
Thus epimorphism means onto (similar) structure.
Sources
- 1974: Thomas W. Hungerford: Algebra ... (previous) ... (next): $\S 1.2$: Definition $2.1$