Abstract: Let K={\mathbb Q}(\alpha) be a number field generated by a complex root \alpha of a monic irreducible polynomial f(x)=x^{18}-m, m\neq \mp 1, is a square free rational integer. We prove that if m \equiv 2 or 3 {\rm(mod }{ 4}) and m\not\equiv \mp 1 {\rm(mod }{ 9}), then the number field K is monogenic. If m \equiv 1 {\rm(mod }{ 4}) or m\equiv 1 {\rm(mod }{ 9}), then the number field K is not monogenic.
Keywords: power integral base; theorem of Ore; prime ideal factorization
DOI: DOI 10.14712/1213-7243.2022.005
AMS Subject Classification: 11R04 11R16 11R21