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

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 ∈ K [ X ₀ , . . . , X m - 1 ] such that f ( ∑ j = 0 m - 1 ξ j X j ) = ∑ 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 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 × ℤ / 2 ℤ × 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.