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 $+$.