Difference between revisions of "Field (mathematics)"

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(correct claim about smallest field)
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A '''field''' is a commutative [[Ring (mathematics)|ring]] which contains a non-zero multiplicative identity and all non-zero elements have multiplicative inverses. Everyday examples of fields include the [[real numbers|real numbers]], [[complex numbers]] and the [[rationals]].  Besides the trivial field, the set of rationals is the smallest number field, so any other number field is an extension field of the rationals.
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A '''field''' is a commutative [[Ring (mathematics)|ring]] which contains a non-zero multiplicative identity and all non-zero elements have multiplicative inverses. Everyday examples of fields include the [[real numbers|real numbers]], [[complex numbers]] and the [[rationals]].  There is a finite field for each power of a prime number.
  
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]

Revision as of 01:17, March 24, 2007

A field is a commutative ring which contains a non-zero multiplicative identity and all non-zero elements have multiplicative inverses. Everyday examples of fields include the real numbers, complex numbers and the rationals. There is a finite field for each power of a prime number.