Chapter 20

Every finite field has nonzero characteristic.

If \((a, b) \sim(c, d)\) means \(a d=b c\), prove that \(\sim\) is an equivalence relation on \(S\).

\text { If the order of } A \text { is } \mathrm{p}^{\mathrm{m}}, \text { where } \mathrm{p} \text { is a prime, the characteristic of } A \text { must be equal to }

If \(A\) has characteristic 3 , and \(5 \cdot a=0\), then \(a=0\).