MAD 4301 Midterm: MAS4301 S97 Test 4
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Instructions: do not write your answers on this paper, use separate answer sheets. This is a closed-book test. (1) complete the following de nitions. (a) a ring is . (b) an abelian group is . (c) let f be a nite eld with q elements. A primitive element of f is (2) give examples of the following. In r, (i) list the elements in the group of units and nd the order of each. (ii) list the zero divisors. (4) prove the following statements. (a) let f be a eld and p(x) f [x]. Let g g. then g has order p if and only if g 6= e. (d) if n is a positive integer, then n factors into a product of prime num- bers.
