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Articles

Minimal pairs, inertia degrees, ramification degrees and implicit constant fields

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Pages 4964-4974 | Received 13 Dec 2021, Accepted 10 May 2022, Published online: 28 May 2022

References

  • Alexandru, V., Popescu, N., Zaharescu, A. (1988). A theorem of characterization of residual transcendental extensions of a valuation. J. Math. Kyoto Univ. 28:579–592.
  • Alexandru, V., Popescu, N., Zaharescu, A. (1990). Minimal pairs of definition of a residual transcendental extension of a valuation. J. Math. Kyoto Univ. 30:207–225.
  • Alexandru, V., Zaharescu, A. (1988). Sur une classe de prolongements à K(x) d’une valuation sur une corp K. Rev. Roumaine Math. Pures Appl. 5:393–400.
  • Bourbaki, N. (1972). Commutative Algebra. Paris: Hermann.
  • Dutta, A. (2022). On the ranks and implicit constant fields of valuations induced by pseudo monotone sequences. J. Pure Appl. Algebra 226(11):107107. DOI: 10.1016/j.jpaa.2022.107107.
  • Dutta, A. (2021). Minimal pairs, minimal fields and implicit constant fields. J. Algebra 588:479–514. DOI: 10.1016/j.jalgebra.2021.09.008.
  • Dutta, A., Kuhlmann, F.-V. (2020). Eliminating tame ramification: generalizations of Abhyankar’s lemma. Pacific J. Math. 307(1):121–136. DOI: 10.2140/pjm.2020.307.121.
  • Kuhlmann, F.-V. (2004). Value groups, residue fields and bad places of rational function fields. Trans. Amer. Math. Soc. 356(11):4559–4600. DOI: 10.1090/S0002-9947-04-03463-4.
  • Kuhlmann, F.-V. (2010). Elimination of ramification I: the generalized stability theorem. Trans. Amer. Math. Soc. 362(11):5697–5727. DOI: 10.1090/S0002-9947-2010-04973-6.
  • Peruginelli, G., Spirito, D. (2021). Extending valuations to the field of rational functions using pseudo-monotone sequences. J. Algebra 586:756–786. DOI: 10.1016/j.jalgebra.2021.07.004.

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