Abstract
Let K be a number field with the ring of integers R and \(L=K(\alpha )\). In this work, we give necessary and sufficient conditions on \(a,\; b,\; s,\; n\) so that the irreducible polynomial \(P(X)=X^{p^n}\,+\,a\,X^{p^s}-b\) of R[X] \((n,s\in {\mathbb {N}},\,\, n\, \,>\,\,s)\) of \(\alpha\) is monogenic. We bring forward a family of monogenic extensions over quadratic fields, as result we give their integral bases over \({\mathbb {Q}}\) and absolute discriminants.
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The authors are highly thankful to the referee of the article for several helpful suggestions and useful detailed comments on the manuscript. The authors would like to thank professor M. E. Charkani for his valuable support.
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Boughaleb, O., Soullami, A. & Sahmoudi, M. On relative monogeneity of a family of number fields defined by \(X^{p^n}+aX^{p^s}-b\). Bol. Soc. Mat. Mex. 29, 5 (2023). https://doi.org/10.1007/s40590-022-00472-1
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DOI: https://doi.org/10.1007/s40590-022-00472-1