Defectless polynomials over henselian fields and inductive valuations

Nathália Moraes de Oliveira; Enric Nart

doi:10.1016/j.jalgebra.2019.08.033

Defectless polynomials over henselian fields and inductive valuations

Nathália Moraes de Oliveira, Enric Nart

Department of Mathematics

Research output: Contribution to journal › Article › Research

6 Citations (Scopus)

Abstract

© 2019 Elsevier Inc. Let (K,v) be a henselian valued field. Let Pdless⊂K[x] be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation ≈ on Pdless, we establish a canonical bijection M→Pdless/≈, where M is a discrete MacLane space, constructed in terms of inductive valuations on K[x] extending v.

Original language	English
Pages (from-to)	270-307
Number of pages	38
Journal	Journal of Algebra
Volume	541
DOIs	https://doi.org/10.1016/j.jalgebra.2019.08.033
Publication status	Published - 1 Jan 2020

Keywords

CONSTRUCTION
Defectless polynomial
Graded algebra of a valuation
Henselian field
Inductive valuation
Key polynomial
MacLane chain
Newton polygon
Residual polynomial operator

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10.1016/j.jalgebra.2019.08.033

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abstract = "{\textcopyright} 2019 Elsevier Inc. Let (K,v) be a henselian valued field. Let Pdless⊂K[x] be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation ≈ on Pdless, we establish a canonical bijection M→Pdless/≈, where M is a discrete MacLane space, constructed in terms of inductive valuations on K[x] extending v.",

keywords = "CONSTRUCTION, Defectless polynomial, Graded algebra of a valuation, Henselian field, Inductive valuation, Key polynomial, MacLane chain, Newton polygon, Residual polynomial operator",

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doi = "10.1016/j.jalgebra.2019.08.033",

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AU - Moraes de Oliveira, Nathália

AU - Nart, Enric

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N2 - © 2019 Elsevier Inc. Let (K,v) be a henselian valued field. Let Pdless⊂K[x] be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation ≈ on Pdless, we establish a canonical bijection M→Pdless/≈, where M is a discrete MacLane space, constructed in terms of inductive valuations on K[x] extending v.

AB - © 2019 Elsevier Inc. Let (K,v) be a henselian valued field. Let Pdless⊂K[x] be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation ≈ on Pdless, we establish a canonical bijection M→Pdless/≈, where M is a discrete MacLane space, constructed in terms of inductive valuations on K[x] extending v.

KW - CONSTRUCTION

KW - Defectless polynomial

KW - Graded algebra of a valuation

KW - Henselian field

KW - Inductive valuation

KW - Key polynomial

KW - MacLane chain

KW - Newton polygon

KW - Residual polynomial operator

UR - http://www.mendeley.com/catalogue/defectless-polynomials-henselian-fields-inductive-valuations

U2 - 10.1016/j.jalgebra.2019.08.033

DO - 10.1016/j.jalgebra.2019.08.033

M3 - Article

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VL - 541

SP - 270

EP - 307

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Defectless polynomials over henselian fields and inductive valuations

Abstract

Keywords

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