# Category:Examples of Fields

This category contains examples of Field (Abstract Algebra) in the context of Abstract Algebra.

A field is a non-trivial division ring whose ring product is commutative.

Thus, let $\struct {F, +, \times}$ be an algebraic structure.

Then $\struct {F, +, \times}$ is a field if and only if:

$(1): \quad$ the algebraic structure $\struct {F, +}$ is an abelian group
$(2): \quad$ the algebraic structure $\struct {F^*, \times}$ is an abelian group where $F^* = F \setminus \set {0_F}$
$(3): \quad$ the operation $\times$ distributes over $+$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Examples of Fields"

The following 9 pages are in this category, out of 9 total.