Quasi-Euclidean subrings of Q[x]

Abstract

Using a nonstandard model of Peano arithmetic, we show that there are quasi-Euclidean subrings of Q[x] which are not k-stage Euclidean for any norm and positive integer k. These subrings can be either PID or non-UFD, depending on the choice of parameters in our construction. In both cases, there are 2^ω such domains up to ring isomorphism.

9 pages

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