Category:Definitions/Ring Homomorphisms

This category contains definitions related to Ring Homomorphisms.
Related results can be found in Category: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, $\forall a, b \in R$:

$\text {(1)}: \quad$

$\ds \map \phi {a + b}$

$=$

$\ds \map \phi a \oplus \map \phi b$

$\text {(2)}: \quad$

$\ds \map \phi {a \circ b}$

$=$

$\ds \map \phi a * \map \phi b$

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

Subcategories

This category has the following 6 subcategories, out of 6 total.

The following 27 pages are in this category, out of 27 total.