Difference between revisions of "Field"
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==Definition== | ==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: | 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: | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
| − | {{Definition|Abstract Algebra}}[[Category: | + | {{Definition|Abstract Algebra|Ring Theory}}[[Category:Types of rings]] |
Latest revision as of 21:29, 19 April 2016
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Most of this page is very old, or was created as a stub, and needs to be brought up to date with the rest of the site, especially such a core AA definition
Definition
A field[1] is a ring, [ilmath]F[/ilmath], that is both commutative and has unity with more than one element is a field if:
- Every non-zero element of [ilmath]F[/ilmath] has a multiplicative inverse in [ilmath]F[/ilmath]
Every field is also an Integral domain[1]
