# Category:Ring Homomorphism from Division Ring is Monomorphism or Zero Homomorphism

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This category contains pages concerning **Ring Homomorphism from Division Ring is Monomorphism or Zero Homomorphism**:

Let $\struct {R, +_R, \circ}$ and $\struct {S, +_S, *}$ be rings whose zeros are $0_R$ and $0_S$ respectively.

Let $\phi: R \to S$ be a ring homomorphism.

If $R$ is a division ring, then either:

- $(1): \quad \phi$ is a monomorphism (that is, $\phi$ is injective)
- $(2): \quad \phi$ is the zero homomorphism (that is, $\forall a \in R: \map \phi a = 0_S$).

## Pages in category "Ring Homomorphism from Division Ring is Monomorphism or Zero Homomorphism"

The following 3 pages are in this category, out of 3 total.