# Category:Examples of Fields

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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 $F^* = F \setminus \set 0$
- $(3): \quad$ the operation $\times$ distributes over $+$.

## Subcategories

This category has only the following subcategory.

### I

## Pages in category "Examples of Fields"

The following 7 pages are in this category, out of 7 total.