Difference between revisions of "Field"

From Maths
Jump to: navigation, search
(Created page with "==Definition== A ''field''<ref name="FAS">Fundamentals of Abstract Algebra - Neal H. McCoy</ref> is a ring, {{M|F}}, that is both commutative and has...")
 
m
 
(3 intermediate revisions by the same user not shown)
Line 1: Line 1:
 +
{{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:
Line 17: Line 18:
 
==References==
 
==References==
 
<references/>
 
<references/>
{{Definition|Abstract Algebra}}[[Category:Type of Ring]]
+
{{Definition|Abstract Algebra|Ring Theory}}[[Category:Types of rings]]

Latest revision as of 21:29, 19 April 2016

Stub grade: A
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
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]

Proof of claims




TODO: Page 96 in[1]


See also

References

  1. 1.0 1.1 1.2 Fundamentals of Abstract Algebra - Neal H. McCoy