Abstract Algebra | A PID that is not a Euclidean Domain

We present an example of a principal ideal domain that is not a Euclidean domain. We follow the outline described in Dummit and Foote. In particular, we show that an integral domain D is a PID if and only if it has a Dedekind-Hasse Norm and that every Euclidean domain has a universal side divisor. Then we show that our example has a Dedekind-Hasse norm but no universal side divisor.

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