On the subfields of cyclotomic function fields

Zhengjun Zhao; Xia Wu

Displaying similar documents to “On the subfields of cyclotomic function fields”

On divisibility of the class number of real octic fields of a prime conductor $p = n^{4} + 16$ by $p$

Stanislav Jakubec (1994)

Archivum Mathematicum

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The aim of this paper is to prove the following Theorem Theorem Let $K$ be an octic subfield of the field $Q (ζ_{p} + ζ_{p}^{- 1})$ and let $p = n^{4} + 16$ be prime. Then $p$ divides $h_{K}$ if and only if $p$ divides $B_{j}$ for some $j = \frac{p - 1}{8}$ , $3 \frac{p - 1}{8}$ , $5 \frac{p - 1}{8}$ , $7 \frac{p - 1}{8}$ .

Polynomial Imaginary Decompositions for Finite Separable Extensions

Adam Grygiel (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let K be a field and let L = K[ξ] be a finite field extension of K of degree m > 1. If f ∈ L[Z] is a polynomial, then there exist unique polynomials $u ₀, . . ., u_{m - 1} \in K [X ₀, . . ., X_{m - 1}]$ such that $f (\sum_{j = 0}^{m - 1} ξ^{j} X_{j}) = \sum_{j = 0}^{m - 1} ξ^{j} u_{j}$ . A. Nowicki and S. Spodzieja proved that, if K is a field of characteristic zero and f ≠ 0, then $u ₀, . . ., u_{m - 1}$ have no common divisor in $K [X ₀, . . ., X_{m - 1}]$ of positive degree. We extend this result to the case when L is a separable extension of a field K of arbitrary characteristic. We also show that the same is true for a formal power series in several...

On divisibility of $h^{+}$ by the prime $5$

Stanislav Jakubec (1994)

Mathematica Slovaca

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On the structure of the 2-Iwasawa module of some number fields of degree 16

Idriss Jerrari, Abdelmalek Azizi (2022)

Czechoslovak Mathematical Journal

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Let $K$ be an imaginary cyclic quartic number field whose 2-class group is of type $(2, 2, 2)$ , i.e., isomorphic to $ℤ / 2 ℤ \times ℤ / 2 ℤ \times ℤ / 2 ℤ$ . The aim of this paper is to determine the structure of the Iwasawa module of the genus field $K^{(*)}$ of $K$ .

On the irreducible factors of a polynomial over a valued field

Anuj Jakhar (2024)

Czechoslovak Mathematical Journal

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We explicitly provide numbers $d$ , $e$ such that each irreducible factor of a polynomial $f (x)$ with integer coefficients has a degree greater than or equal to $d$ and $f (x)$ can have at most $e$ irreducible factors over the field of rational numbers. Moreover, we prove our result in a more general setup for polynomials with coefficients from the valuation ring of an arbitrary valued field.

Displaying similar documents to “On the subfields of cyclotomic function fields”

On divisibility of the class number of real octic fields of a prime conductor p = n 4 + 16 by p

Polynomial Imaginary Decompositions for Finite Separable Extensions

On divisibility of h + by the prime 5

On the structure of the 2-Iwasawa module of some number fields of degree 16

On the irreducible factors of a polynomial over a valued field

On divisibility of the class number of real octic fields of a prime conductor $p = n^{4} + 16$ by $p$

On divisibility of $h^{+}$ by the prime $5$