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Keywords:
power integral basis; theorem of Ore; prime ideal factorization; common index divisor
power integral basis; theorem of Ore; prime ideal factorization; common index divisor
Summary:
Let $K = \mathbb {Q} (\alpha ) $ be a pure number field generated by a complex root $\alpha $ of a monic irreducible polynomial $ F(x) = x^{2^r\cdot 3^k\cdot 7^s} -m \in \mathbb{Z}[x]$, where $r$, $k$, $s$ are three positive natural integers. The purpose of this paper is to study the monogenity of $K$. Our results are illustrated by some examples.
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