Key polynomials for simple extensions of valued fields
Journal of Singularities, Tome 25 (2022), pp. 197-267
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In this paper we present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e and reminiscent of approximate roots of Abhyankar and Moh. Given a simple transcendental extension of valued fields, we associate to it a countable well-ordered set of polynomials called key polynomials. We define limit key polynomials and give explicit formulae for them. We give an explicit bound on the order type of the set of key polynomials.
@article{10_5427_jsing_2022_25k,
author = {F. J. Herrera Govantes and W. Mahboub and M. A. Olalla Acosta, and M. Spivakovsky},
title = {Key polynomials for simple extensions of valued fields},
journal = {Journal of Singularities},
pages = {197--267},
publisher = {mathdoc},
volume = {25},
year = {2022},
doi = {10.5427/jsing.2022.25k},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.25k/}
}
TY - JOUR AU - F. J. Herrera Govantes AU - W. Mahboub AU - M. A. Olalla Acosta, AU - M. Spivakovsky TI - Key polynomials for simple extensions of valued fields JO - Journal of Singularities PY - 2022 SP - 197 EP - 267 VL - 25 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.25k/ DO - 10.5427/jsing.2022.25k ID - 10_5427_jsing_2022_25k ER -
%0 Journal Article %A F. J. Herrera Govantes %A W. Mahboub %A M. A. Olalla Acosta, %A M. Spivakovsky %T Key polynomials for simple extensions of valued fields %J Journal of Singularities %D 2022 %P 197-267 %V 25 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.25k/ %R 10.5427/jsing.2022.25k %F 10_5427_jsing_2022_25k
F. J. Herrera Govantes; W. Mahboub; M. A. Olalla Acosta,; M. Spivakovsky. Key polynomials for simple extensions of valued fields. Journal of Singularities, Tome 25 (2022), pp. 197-267. doi: 10.5427/jsing.2022.25k
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