An Eisenstein Criterion for Noncommutative Polynomials
An Eisenstein Criterion for Noncommutative Polynomials
An analogue of the Eisenstein irreducibility criterion is developed for linear differential operators, or, more generally, noncommutative polynomials, and is applied to a few simple examples.Introduction.The question of the irreducibility of an ordinary linear differential operator is of interest in the Picard-Vessiot theory (see Kolchin [1, §22]).Indeed, the operator is …