\begin{definition}[Definition:Field (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''' {{iff}}:
:$(1): \quad$ 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 $+$.
This definition gives rise to the '''field axioms''', as follows:
\end{definition}