Talk:Algebraic number: Difference between revisions

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imported>Catherine Woodgold
(characteristic?)
imported>Greg Woodhouse
(characteristic? - definition)
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In this sentence:  ''"The algebraic numbers form a [[field (mathematics)|field]]; in fact, they are the smallest [[algebraically closed field]] with characteristic 0. "'' I don't know what "characteristic 0" means.  Perhaps a definition or a link would be helpful.  --[[User:Catherine Woodgold|Catherine Woodgold]] 21:23, 28 April 2007 (CDT)
In this sentence:  ''"The algebraic numbers form a [[field (mathematics)|field]]; in fact, they are the smallest [[algebraically closed field]] with characteristic 0. "'' I don't know what "characteristic 0" means.  Perhaps a definition or a link would be helpful.  --[[User:Catherine Woodgold|Catherine Woodgold]] 21:23, 28 April 2007 (CDT)
:Oh, sorry. if 1 + 1 = 0 the characteistic is said to be 2, if 1 + 1 + 1 = 0 the characteristic is said to be 3, and forth. If there is no n such that <math>\scriptstyle n \cdot 1 = 0</math>, we say the characteristic is 0. A field of positive characteristic need not be finite. Two examples are the algebraic closure of <math>\mathbb{Z}_2</math> (usually written <math>\mathbb{F}_2</math> when the emphasis is on being a field). Another basic example is the field of rational functions in one variable, <math>\mathbb{F}_2 [x]</math>. Fields of positive characteristic are important in applications to number theory. [[User:Greg Woodhouse|Greg Woodhouse]] 22:04, 28 April 2007 (CDT)

Revision as of 21:04, 28 April 2007


Article Checklist for "Algebraic number"
Workgroup category or categories Mathematics Workgroup [Categories OK]
Article status Stub: no more than a few sentences
Underlinked article? No
Basic cleanup done? Yes
Checklist last edited by -Versuri 11:56, 26 March 2007 (CDT)

To learn how to fill out this checklist, please see CZ:The Article Checklist.





things to add:

  • links to "rational number" and "polynomial"
  • a couple of examples - and put in the polynomial that sqrt(2) satisfies
  • mention that some, but not all, algebraic numbers can be expressed using radicals - mention and link Galois
  • the link to "countable" should probably point to a new page on cardinality
I think the link should be to Countable set. Andres Luure 03:09, 26 March 2007 (CDT)

characteristic?

In this sentence: "The algebraic numbers form a field; in fact, they are the smallest algebraically closed field with characteristic 0. " I don't know what "characteristic 0" means. Perhaps a definition or a link would be helpful. --Catherine Woodgold 21:23, 28 April 2007 (CDT)

Oh, sorry. if 1 + 1 = 0 the characteistic is said to be 2, if 1 + 1 + 1 = 0 the characteristic is said to be 3, and forth. If there is no n such that , we say the characteristic is 0. A field of positive characteristic need not be finite. Two examples are the algebraic closure of (usually written when the emphasis is on being a field). Another basic example is the field of rational functions in one variable, . Fields of positive characteristic are important in applications to number theory. Greg Woodhouse 22:04, 28 April 2007 (CDT)