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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


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