El Fadil, Lhoussain Prime ideal factorization and \(p\)-integral basis of quintic number fields defined by \(X^5+aX+b\). (English) Zbl 1407.11145 Gulf J. Math. 6, No. 4, 1-13 (2018). Summary: Based on Newton polygon techniques, for every prime integer \(p\), a \(p\)-integral basis of \(\mathbb{Z}_K\), and the factorization of the principal ideal \(p\mathbb{Z}_K\) into prime ideals of \(\mathbb{Z}_K\) are given, where \(K\) is a quintic number field defined by an irreducible trinomial \(X^5+aX+b\in\mathbb{Z}[X]\). Cited in 1 ReviewCited in 1 Document MSC: 11Y40 Algebraic number theory computations 11R16 Cubic and quartic extensions Keywords:prime ideal factorization; Newton polygons; \(p\)-regular polynomial; quartic fields PDFBibTeX XMLCite \textit{L. El Fadil}, Gulf J. Math. 6, No. 4, 1--13 (2018; Zbl 1407.11145) Full Text: Link