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Fields and generators

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Polynomial Ring. See attached file for full problem description.

1. Construct the fields of the following orders (a) 9 (b) 49 (c) 8 (d) 81(you may exhibit these as F[x]/(f(x))) for some F and f)
2. For each of the fields constructed in (1) exhibit a generator foe the (cyclic) multiplicative group of nonzero elements.

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Solution Summary

This shows how to construct fields of given orders and use these fields to exhibit a generator for a multiplicative group.

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1. Construct the fields of the following orders (a) 9 (b) 49 (c) 8 (d) 81(you may exhibit these as F[x]/(f(x))) for some F and f)
2. For each of the fields constructed in (1) exhibit a generator foe the (cyclic) multiplicative group of nonzero elements.

(a) . The multiplicative group ...

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