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On the unramified extensions of the prime cyclotomic number field and its quadratic extensions
, 1991 openaire +1 more source
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Cyclotomic Extensions of Diagram Algebras
Communications in Algebra, 2008A uniform approach to cyclotomic extensions of diagram algebras is given, focussing on cellular structures. Cyclotomic Temperley–Lieb algebras, cyclotomic Brauer algebras and cyclotomic walled Brauer algebras are discussed as examples.
Steffen Koenig
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A Leopoldt-Type Result for Rings of Integers of Cyclotomic Extensions
Canadian Mathematical Bulletin, 1995 AbstractLet p be a prime number and let m, r denote positive integers with r ≥ 1 if p > 3 (resp. r ≥ 2 if p = 2) and m ≥ 1. We put and Γ = Gd1(N/M). Then the associated order of N/M is the unique maximal order M in the group ring MΓ and ON is a free, rank one module over M. A generator of ON over M is explicitly given.
Bley, Werner, W. Bley
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On the unramified Kummer extensions of quadratic extensions of the prime cyclotomic number field
Archiv Der Mathematik, 1991exaly +2 more sources
Class numbers in cyclotomic Zp-extensions
Journal of Number Theory, 2015 . For any prime p and any positive integer n, let Bp,n denote the nth layer of the cyclotomic Zp-extension over the rationals. Based on the heuristics of Cohen and Lenstra, and refined by new results on class numbers of particular Bp,n, we provide ...
John C Miller
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Cyclotomic units in z p -extensions
Israel Journal of Mathematics, 1991LetK0 be the maximal real subfield of the field generated by thep-th root of 1 over ℚ, andK∞ be the basic Zp-extension ofK0 for a fixed odd primep. LetKn be itsn-th layer of this tower. For eachn, we denote the Sylowp-subgroup of the ideal class group ofKn byAn, and that ofEnCn byBn, whereEn (resp.Cn) is the group of units (resp. cyclotomic units ofKn.
Jae Moon Kim, Sunghan Bae, In-Sok Lee
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ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
Mathematics of the USSR-Izvestiya, 1980This paper is devoted to the realization of certain types of Chevalley groups as the Galois group of extensions of certain cyclotomic fields. In addition, a criterion for an algebraic curve to be defined over an algebraic number field is given. Bibliography: 11 titles.
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An extension of binary cyclotomic sequences having order 2lt
Discrete Mathematics, Algorithms and Applications, 2022Several reasonably cyclotomic sequences are constructed by cyclotomic classes having good pseudo-randomness property. In this paper, we derive the linear complexity of an extended binary cyclotomic sequences of order [Formula: see text] over finite field having period [Formula: see text].
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2001
In this chapter we shall describe the work of Gauss and Lagrange on the resolution by radicals of cyclotomic polynomials. Then we will describe some of the work of Jacobi and Kummer on the ideal theory of rings of cyclotomic integers.
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In this chapter we shall describe the work of Gauss and Lagrange on the resolution by radicals of cyclotomic polynomials. Then we will describe some of the work of Jacobi and Kummer on the ideal theory of rings of cyclotomic integers.
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On the maximal unramified pro-2-extension of certain cyclotomic $$\mathbb {Z}_2$$-extensions
Periodica Mathematica Hungarica, 2020Let \({k}\) be a number field and let \({k}_{\infty}\) be the cyclotomic \({\mathbb{Z}}_2\)-extension of \({k}\). Let \(A({k}_n)\) be the \(2\)-Sylow subgroup of the ideal class group of the \(n\)-layer \({k}_n\) of \({k}_{\infty}/{k}\). Let \({\mathcal{L}}({k}_{\infty})\) denote the maximal unramified pro-extension of \({k}_{\infty}\) and \({\mathcal ...
Abdelmalek Azizi +2 more
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