# Category:Ring Homomorphisms

Jump to navigation
Jump to search

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

\((1):\quad\) | \(\displaystyle \map \phi {a + b}\) | \(=\) | \(\displaystyle \map \phi a \oplus \map \phi b\) | ||||||||||

\((2):\quad\) | \(\displaystyle \map \phi {a \circ b}\) | \(=\) | \(\displaystyle \map \phi a * \map \phi b\) |

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.

### F

### R

## Pages in category "Ring Homomorphisms"

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