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==Definition==
A ''field''<ref name="FAS">Fundamentals of Abstract Algebra - Neal H. McCoy</ref> is a [[ring]], {{M|F}}, that is both [[Commutative ring|commutative]] and has [[Ring with unity|unity]] with more than one element is a field if:
* Every non-zero element of {{M|F}} has a multiplicative inverse in {{M|F}}
Every ''field'' is also an [[Integral domain]]<ref name="FAS"/>
==Proof of claims==
{{Begin Inline Theorem}}
* Every field is an [[Integral domain]]
{{Begin Inline Proof}}
{{Todo|Page 96 in<ref name="FAS"/>}}
{{End Proof}}{{End Theorem}}
==See also==
* [[Vector space]]
* [[Ring]]
* [[Integral domain]]
* [[Types of rings]]
* [[Characteristic of a ring]]
==References==
<references/>
{{Definition|Abstract Algebra}}[[Category:Types of rings]]