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On the irreducible factors of a polynomial over a valued field

Anuj Jakhar (2024)

Czechoslovak Mathematical Journal

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.

On valuations of nearfields

Dalibor Klucký, Libuše Marková (1983)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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