Results 11 to 20 of about 130 (120)
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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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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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).
Bandini A., Bars F., Coscelli E.
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Prime decomposition in the anti-cyclotomic extension [PDF]
Mathematics of Computation, 2007 For an imaginary quadratic number field K K and an odd prime number
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On Nilpotent Extensions of ∞-Categories and the Cyclotomic Trace
International Mathematics Research Notices, 2021 AbstractWe do three things in this paper: (1) study the analog of localization sequences (in the sense of algebraic $K$-theory of stable $\infty $-categories) for additive $\infty $-categories, (2) define the notion of nilpotent extensions for suitable $\infty $-categories and furnish interesting examples such as categorical square-zero extensions, and
Elden Elmanto, Vladimir Sosnilo
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A Result of Bass on Cyclotomic Extension Fields [PDF]
Proceedings of the American Mathematical Society, 1970 In [1] Bass stated the result given below as Proposition 1 and derived some consequences. His proof of the proposition itself, however, contains a gap; Lemmas 2 and 3 are false as stated. The purpose of this note is to fill the gap by proving the slightly stronger Proposition 2. We retain the notation of [1]. In particular k,,=k(Dm) where A;m = e2rilm.
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Minimal splitting fields in cyclotomic extensions [PDF]
Proceedings of the American Mathematical Society, 1983 Suppose G G is a finite group of exponent
Spiegel, Eugene, Trojan, Allan
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Radical and cyclotomic extensions of the rational numbers [PDF]
Proceedings of the American Mathematical Society, 2007 The principal result in this article is the proof that the Galois closure \(E/\mathbb{Q}\) of a radical extension of the rational numbers \(\mathbb{Q}\) (i.e. an extension \(R = \mathbb{Q}[\alpha]\), where \(\alpha^n \in \mathbb{Q}\) for some positive integer \(n\)) contains a (maximal) cyclotomic extension \(K\) of \(\mathbb{Q}\) whose index in \(E ...
Gluck, David, Isaacs, I. M.
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Artin--Schreier and Cyclotomic Extensions
, 2013 10 ...
Salas-Torres, Julio Cesar +2 more
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Iwasawa main conjecture for the Carlitz cyclotomic extension and applications [PDF]
Mathematische Annalen, 2019 Section 3 entirely ...
Bruno Anglès +3 more
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