Sch\"onemann-Eisenstein-Dumas-type irreducibility conditions that use arbitrarily many prime numbers
Number Theory
2014-03-24 v2
Abstract
The famous irreducibility criteria of Sch\"onemann-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 Sch\"onemann-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.
Keywords
Cite
@article{arxiv.1304.0874,
title = {Sch\"onemann-Eisenstein-Dumas-type irreducibility conditions that use arbitrarily many prime numbers},
author = {Nicolae Ciprian Bonciocat},
journal= {arXiv preprint arXiv:1304.0874},
year = {2014}
}
Comments
34 pages; 15 figures; corrected typos and references; a shortened version of this paper was accepted for publication in Communications in Algebra