2.4 Fields

2.4 Fields

Definition 2.4.1 A field is a commutative ring in which all non-zero elements have mul-

tiplicative inverses.

Theorem 2.4.1 Zn is a field (under the usual operations of addition and multiplication

modulo n) if and only if n is a prime number. If n is prime, then Zn has characteristic n.

Theorem 2.4.2 If the characteristic n of a field is not 0, then n is a prime number.