# Category:Ring Homomorphisms

This category contains results about Ring Homomorphisms.
Definitions specific to this category can be found in Definitions/Ring Homomorphisms.

Let $\struct {R, +, \circ}$ and $\struct{S, \oplus, *}$ be rings.

Let $\phi: R \to S$ be a mapping such that both $+$ and $\circ$ have the morphism property under $\phi$.

That is, $\forall a, b \in R$:

 $\text {(1)}: \quad$ $\displaystyle \map \phi {a + b}$ $=$ $\displaystyle \map \phi a \oplus \map \phi b$ $\text {(2)}: \quad$ $\displaystyle \map \phi {a \circ b}$ $=$ $\displaystyle \map \phi a * \map \phi b$

Then $\phi: \struct {R, +, \circ} \to \struct {S, \oplus, *}$ is a ring homomorphism.

## Subcategories

This category has the following 8 subcategories, out of 8 total.

## Pages in category "Ring Homomorphisms"

The following 22 pages are in this category, out of 22 total.