Abstract

We consider a concrete family of 2-towers (Q(x(n)))(n) of totally real algebraic numbers for whichwe prove that, for each n, Z[x(n)] is the ringof integers ofQ(x(n)) if and only if the constant term of theminimal polynomial of x(n) is square-free. We apply our characterization to produce new examples of monogenic number fields, which can be of arbitrary large degree under the ABC-Conjecture.