On the monogenity of quartic number fields defined by $x^4+a{x}^2+b$

Abstract

For any quartic number field $K$ generated by a root $\alpha$ of an irreducible trinomial of type $x^4+a{x}^2+b\in Z[x]$, we characterize when $Z[\alpha ]$ is integrally closed. Also for $p=2,3$, we explicitly give the highest power of $p$ dividing $i(K)$, the common index divisor of $K$. For a wide class of monogenic trinomials of this type we prove that up to equivalence there is only one generator of power integral bases in $K=Q(\alpha )$. We illustrate our statements with a series of examples.

arXiv admin note: text overlap with arXiv:2202.09342, arXiv:2202.04417, arXiv:2112.01133, arXiv:2203.13353