Difference between revisions of "Field (mathematics)"
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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]]. | + | 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. |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 21:18, March 15, 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. 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.