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Quasi-ordered rings : A uniform approach to orderings and valuations

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2018

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https://doi.org/10.1080/00927872.2018.1459651
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http://arxiv.org/abs/1706.04533v3

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Communications in Algebra. 2018, 46(11), pp. 4978-4984. ISSN 0092-7872. eISSN 1532-4125. Available under: doi: 10.1080/00927872.2018.1459651

Zusammenfassung

A quasi-order on a set S is a binary, reflexive and transitive relation on S. In [3 Fakhruddin, S. M. (1987). Quasi-ordered fields. J. Pure Appl. Algebra 45:207–210.[Crossref], [Web of Science ®], [Google Scholar]], Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered field or else a valued field. Hence, quasi-ordered fields are very well suited to treat ordered and valued fields simultaneously. The aim of the present paper is to prove that an analogous dichotomy holds for commutative rings with 1 as well.

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Fachgebiet (DDC)
510 Mathematik

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Commutative rings, ordered rings, quasi-orders, real algebra, valued rings

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ISO 690MÜLLER, Simon, 2018. Quasi-ordered rings : A uniform approach to orderings and valuations. In: Communications in Algebra. 2018, 46(11), pp. 4978-4984. ISSN 0092-7872. eISSN 1532-4125. Available under: doi: 10.1080/00927872.2018.1459651
BibTex
@article{Muller2018Quasi-43510,
  year={2018},
  doi={10.1080/00927872.2018.1459651},
  title={Quasi-ordered rings : A uniform approach to orderings and valuations},
  number={11},
  volume={46},
  issn={0092-7872},
  journal={Communications in Algebra},
  pages={4978--4984},
  author={Müller, Simon}
}
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