On the irreducible factors of a polynomial

Jakhar, Anuj

doi:10.1090/proc/14856

On the irreducible factors of a polynomial
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Proc. Amer. Math. Soc. 148 (2020), 1429-1437 Request permission

Abstract:

In 2013, S. H. Weintraub proved a generalization of the classical Eisenstein irreducibility criterion by providing a bound on the degrees of factors of a polynomial with integer coefficients (see [Proc. Amer. Math. Soc. 141(4) (2013), pp. 1159–1160]). In this paper, we extend this result with a much weaker hypothesis in a more general setup for polynomials having coefficients from the valuation ring of arbitrary valued field. Moreover, when a polynomial $f(x)$ has coefficients from the valuation ring of a henselian valued field $K$, then we give more precise information about an irreducible factor of $f(x)$ over $K$.

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