Category:Field Homomorphisms

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

Let $\struct {F, +, \times}$ and $\struct {K, \oplus, \otimes}$ be fields.

Let $\phi: F \to K$ be a mapping such that both $+$ and $\times$ have the morphism property under $\phi$.

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

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

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

$=$

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

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

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

$=$

$\ds \map \phi a \otimes \map \phi b$

Then $\phi: \struct {F, +, \times} \to \struct {K, \oplus, \otimes}$ is a field homomorphism.

Subcategories

This category has the following 5 subcategories, out of 5 total.

The following 6 pages are in this category, out of 6 total.