On the irreducible factors of a polynomial over a valued field

Anuj Jakhar

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 2, page 367-375
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Jakhar, Anuj. "On the irreducible factors of a polynomial over a valued field." Czechoslovak Mathematical Journal 74.2 (2024): 367-375. <http://eudml.org/doc/299509>.

@article{Jakhar2024,
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.},
author = {Jakhar, Anuj},
journal = {Czechoslovak Mathematical Journal},
keywords = {irreducibility; Eisenstein criterion; polynomial},
language = {eng},
number = {2},
pages = {367-375},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the irreducible factors of a polynomial over a valued field},
url = {http://eudml.org/doc/299509},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Jakhar, Anuj
TI - On the irreducible factors of a polynomial over a valued field
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 2
SP - 367
EP - 375
AB - 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.
LA - eng
KW - irreducibility; Eisenstein criterion; polynomial
UR - http://eudml.org/doc/299509
ER -

References

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