Category:Definitions/Field Homomorphisms

This category contains definitions related to Field Homomorphisms.
Related results can be found in Category: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.

Pages in category "Definitions/Field Homomorphisms"

The following 2 pages are in this category, out of 2 total.