Difference between revisions of "Field"
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| − | {{Stub page|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}} | + | {{Stub page|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|grade=A}} |
==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: | ||
Latest revision as of 21:29, 19 April 2016
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Contents
[hide]Definition
A field[1] is a ring, F, that is both commutative and has unity with more than one element is a field if:
- Every non-zero element of F has a multiplicative inverse in F
Every field is also an Integral domain[1]
Proof of claims
See also
References
- ↑ Jump up to: 1.0 1.1 1.2 Fundamentals of Abstract Algebra - Neal H. McCoy
