Exercises in Field Theory and Galois Theory
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چکیده
1. Algebraic extensions (1) Let F be a finite field with characteristic p. Prove that |F | = p n for some n. (2) Using f (x) = x 2 + x − 1 and g(x) = x 3 − x + 1, construct finite fields containing 4, 8, 9, 27 elements. Write down multiplication tables for the fields with 4 and 9 elements and verify that the multiplicative groups of these fields are cyclic.
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