Let denote the ring of algebraic integers of an algebraic number field where the algebraic integer is a root of an irreducible quadrinomial belonging to with . We give necessary and sufficient conditions involving only for a prime to divide the index of the subgroup in . As a consequence, we obtain necessary and sufficient conditions for to be equal to . Moreover, when , we provide an explicit formula for the index in some cases.
"On primes dividing the index of a quadrinomial." Rocky Mountain J. Math. 50 (6) 2117 - 2125, December 2020. https://doi.org/10.1216/rmj.2020.50.2117