On the extensions of discrete valuations in number fields

Rok, strany: 2019, 1009 - 1022

Let $K$ be a number field defined by a monic irreducible polynomial $F(X) \in \Z[X]$, $p$ a fixed rational prime, and $ν_p$ the discrete valuation associated to $p$. Assume that $\overline{F}(X)$ factors modulo $p$ into the product of powers of $r$ distinct monic irreducible polynomials. We present in this paper a condition, weaker than the known ones, which guarantees the existence of exactly $r$ valuations of $K$ extending $ν_p$. We further specify the ramification indices and residue degrees of these extended valuations in such a way that generalizes the known estimates. Some useful remarks and computational examples are also given to highlight some improvements due to our result.

ISO 690:

Deajim, A., Fadil, L. 2019. On the extensions of discrete valuations in number fields. In Mathematica Slovaca, vol. 69, no.5, pp. 1009-1022. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0285

APA:

Deajim, A., Fadil, L. (2019). On the extensions of discrete valuations in number fields. Mathematica Slovaca, 69(5), 1009-1022. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0285

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava