Schönemann-Eisenstein-Dumas-type irreducibility conditions that use arbitrarily many prime numbers

Abstract

The famous irreducibility criteria of Schönemann-Eisenstein and Dumas rely on information on the divisibility of the coefficients of a polynomial by a single prime number. In this paper we provide several irreducibility criteria of Schönemann-Eisenstein-Dumas-type for polynomials with integer coefficients, criteria that are given by some divisibility conditions for their coefficients with respect to arbitrarily many prime numbers. A special attention will be paid to those irreducibility criteria that require information on the divisibility of the coefficients by two distinct prime numbers.

arXiv comment34 pages; 15 figures; corrected typos and references; a shortened version of this paper was accepted for publication in Communications in Algebra