MONOGENITY OF THE COMPOSITION OF POLYNOMIALS

Abstract One of the important problems in algebraic number theory is to study the monogenity of number fields. Monogenic number fields arise from the roots of monogenic polynomials. In this article, we deal with the problem of monogenity of the composition of two monic polynomials having integer coefficients. We provide necessary and sufficient conditions for the composition to be monogenic together with a further sufficient condition. At the end of the paper, we construct an infinite tower of monogenic number fields.