Arithmetic of Rikuna's generic cyclic polynomial and generalization of Kummer theory

DOI10.1007/s00229-004-0460-2zbMath1093.11068OpenAlexW2066600246MaRDI QIDQ1882774

Toru Komatsu

Publication date: 1 October 2004

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-004-0460-2

zbMATH Keywords

generic polynomial

Mathematics Subject Classification ID

Galois theory (11R32) Special polynomials in general fields (12E10) Other abelian and metabelian extensions (11R20)

Related Items (13)

Tschirnhausen transformation of a cubic generic polynomial and a \(2\)-dimensional involutive Cremona transformation ⋮ RAMIFICATION IN KUMMER EXTENSIONS ARISING FROM ALGEBRAIC TORI ⋮ On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields ⋮ Cyclic cubic field with explicit Artin symbols ⋮ Twisted Kummer and Kummer-Artin-Schreier theories ⋮ On 2-adic Lie iterated extensions of number fields arising from a Joukowski map ⋮ Rikuna's generic cyclic polynomial and the monogenity ⋮ Discriminants of simplest \(3^n\)-tic extensions ⋮ On the simplest sextic fields and related Thue equations ⋮ On the Simplest Quartic Fields and Related Thue Equations ⋮ A family of geometric operators on triangles with two complex variables ⋮ Generalized Kummer theory and its applications ⋮ Kummer theory for norm algebraic tori

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