English

Quasi-Euclidean subrings of Q[x]

Rings and Algebras 2014-10-27 v1

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^{\omega} such domains up to ring isomorphism.

Keywords

Cite

@article{arxiv.1410.6746,
  title  = {Quasi-Euclidean subrings of Q[x]},
  author = {Petr Glivický and Jan Šaroch},
  journal= {arXiv preprint arXiv:1410.6746},
  year   = {2014}
}

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9 pages