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Please work on the division algorithm. We'll be presenting it on Monday. Also, complete your 3rd write up before class. You can pick any problem from week 4, or one from week 3.

We'll finish up any proofs we didn't finish from Friday (So Sam's got #5 and Nick/Others have #2). Then we'll look at some examples of $Z[\sqrt{d}]$ and $Q[\sqrt{d}]$, as well as $Z_p[\sqrt{d}]$. We'll also spend some more time looking at factor rings over IDs versus fields. I would like you to see examples of integral domains where unique factorization breaks down (so solving algebraic equations becomes nightmarish).

  1. Construct a field with 8 elements.

For more problems, see AllProblems