2. Let K be a subfield of F. Then Char(K) =Char(F). 3. The characteristic of a finite ring R divides R. (Hint: Lagrange'

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2 Let K Be A Subfield Of F Then Char K Char F 3 The Characteristic Of A Finite Ring R Divides R Hint Lagrange 1 (26.9 KiB) Viewed 32 times

2. Let K be a subfield of F. Then Char(K) =Char(F). 3. The characteristic of a finite ring R divides R. (Hint: Lagrange's Theorem) 4. Let F be a field of order 2", then Char(F) = 2. The Char(F) is equal to the additive order of 1F, from the result of the Lagrange Theorem, |F|1F = 0f. Thus 0 (1F) | 2". Since the only prime divisor of 2" is 2, Char(F) = 2.