Definition:Ring Endomorphism

Definition

Let $\struct {R, +, \circ}$ be a ring.

Let $\phi: R \to R$ be a (ring) homomorphism from $R$ to itself.

Then $\phi$ is a ring endomorphism.

Also see

• Endomorphism

• Results about ring endomorphisms can be found here.

Linguistic Note

The word endomorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix endo- (from ἔνδον') meaning inner or internal.

Thus endomorphism means internal structure.

Sources

• 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): $\S 2.2$: Homomorphisms: Definition $2.4$