Results 11 to 20 of about 545 (160)
On the defining polynomials of maximal real cyclotomic extensions
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2008 Summary: The aim of this paper is to show that the simplest techniques of linear algebra allow us to make explicit the defining equations of the maximal real cyclotomic extensions \(\mathbb Q(\zeta+\zeta^ {-1})\) of \(\mathbb Q(\zeta)\), where \(\zeta\) stands for a primitive \(p^ \nu\)-th root of unity with \(p\) a rational prime and \(\nu\) any ...
A Arenas
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Fitting ideals of class groups in Carlitz–Hayes cyclotomic extensions [PDF]
Journal of Number Theory, 2022 We generalize some results of Greither and Popescu to a geometric Galois cover $X\rightarrow Y$ which appears naturally for example in extensions generated by $\mathfrak{p}^n$-torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz-Hayes cyclotomic extensions of global fields of positive characteristic).
Andrea Bandini +2 more
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Cyclotomic Z2-extensions of J-fields
Journal of Number Theory, 1982 AbstractHurwitz-type relations of Iwasawa's λ2−-invariants and the 2-ranks of the “narrow” ideal class groups in the 2-extensions of J-fields are given under the assumption of the vanishing of μ2-invariants.
Kida, Yûji
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A note on quadratic cyclotomic extensions
, 2022 This paper provides two characterizations of the primitive roots of unity in quadratic cyclotomic extensions over arbitrary fields. Firstly, we introduce a mapping from $\mathbb{N}$ to $\mathbb{N}$ crucial for describing these roots, closely tied to their order over the field.
Marques, Sophie, Mrema, Elizabeth
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Chromatic cyclotomic extensions
Geometry & Topology, 2023 We construct Galois extensions of the T(n)-local sphere, lifting all finite abelian Galois extensions of the K(n)-local sphere. This is achieved by realizing them as higher semiadditive analogues of cyclotomic extensions. Combining this with a general form of Kummer theory, we lift certain elements from the K(n)-local Picard group to the T(n)-local ...
Carmeli, S. +2 more
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Extended Genus Fields of Abelian Extensions of Rational Function Fields
AxiomsIn this paper, we obtain the extended genus field of a finite abelian extension of a global rational function field. We first study the case of a cyclic extension of prime power degree. For the general case, we use the fact that the extended genus fields
Juan Carlos Hernandez-Bocanegra +1 more
doaj +2 more sources
l-Extensions of CM-fields and cyclotomic invariants
Journal of Number Theory, 1980 AbstractThe Hurwitz type relation of Iwasawa's λ−-invariants in l-extensions of CM-fields is given under the assumption of the vanishing of μ−-invariants.
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When is a 2-Power Cyclotomic Extension cyclic?
, 2023 This paper characterizes the cyclicity property of $2$-power cyclotomic extensions through various means: the structure of the Galois groups, the nature of their subextensions, tower decompositions, and, most importantly, specific conditions on the base field.
Marques, Sophie, Mrema, Elizabeth
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EXPLICIT KUMMER GENERATORS FOR CYCLOTOMIC EXTENSIONS [PDF]
JP Journal of Algebra, Number Theory and Applications, 2022 Summary: If \(p\) is a prime number congruent to 1 modulo 3, then we explicitly describe an element of the cyclotomic field \(\mathbb Q(\zeta_3)\) whose third root generates the cubic subextension of \(\mathbb Q(\zeta_{3p})/\mathbb Q(\zeta_3)\). Similarly, if \(p\) is a prime number congruent to 1 modulo 4, then we explicitly describe an element of the
Hörmann, Fritz +3 more
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Cyclotomic Units in Zp-Extensions
Journal of Algebra, 1995 Kucera, R., Nekovar, J.
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