Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, first online, pp. 1-9

On the irreducible factors of a polynomial over a valued field

Anuj Jakhar

Received October 6, 2022. Published online April 8, 2024.

Abstract: 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.

Keywords: irreducibility; Eisenstein criterion; polynomial

Classification MSC: 12E05, 11R09, 12J10

DOI: 10.21136/CMJ.2024.0451-22

PDF available at: Institute of Mathematics CAS

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Affiliations: Anuj Jakhar, Department of Mathematics, Indian Institute of Technology Madras, NAC Rd, Chennai, Tamil Nadu 600036, India, e-mail: anujjakhar@iitm.ac.in

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