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{{stub}}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]], [[complex numbers]] and the [[rationals]].  There is a unique (up to [[isomorphism]]) finite field of [[characteristic]] <math>p</math> for each power of a prime number <math>p</math>.

{{stub}}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]], [[complex numbers]] and the [[rationals]].  The [[characteristic]] of a field must be either 0 or a [[prime number]] ''p''. For each prime number ''p'' and positive integer ''n'', there is a unique (up to [[isomorphism]]) finite field of [[characteristic]] ''p'' whose [[cardinality]] is ''pⁿ''. A field of characteristic 0 is necessarily infinite.

[[Category:Algebra]]

[[Category:Algebra]]