Category:Ring Homomorphism from Field is Monomorphism or Zero Homomorphism

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


Let $\struct {F, +_F, \circ}$ be a field whose zero is $0_F$.

Let $\struct {S, +_S, *}$ be a ring whose zero is $0_S$.

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


Then either:

$(1): \quad \phi$ is a monomorphism (that is, $\phi$ is injective)

or

$(2): \quad \phi$ is the zero homomorphism (that is, $\forall a \in F: \map \phi a = 0_S$).

Pages in category "Ring Homomorphism from Field is Monomorphism or Zero Homomorphism"

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