An Irreducibility Test for Polynomials whose Coefficients are Algebraic Integers

Abstract

For a non-zero algebraic integer α, let ℚ(α) denote the simple extension of the field of rational numbers ℚ. ℤ[α] is the smallest subring of ℚ(α) containing both ℤ and α. In this article, we present an account for testing irreducibility of a given polynomial with coefficients in ℤ[α] over the field ℚ(α).