Evertse, Jan-Hendrik A survey on monogenic orders. (English) Zbl 1249.11102 Publ. Math. Debr. 79, No. 3-4, 411-422 (2011). Summary: Recall that an order \(\mathcal O\) in an algebraic number field \(K\) is called monogenic if it is generated by one element, i.e., there is an \(\alpha\) with \(\mathbb Z[\alpha ]=\mathcal O\).By work of K. Győry [Publ.Math.Debrecen 23, 141–165 (1976; Zbl 0354.10041)] there are, up to a suitable equivalence, only finitely many \(\alpha\) such that \(\mathbb Z[\alpha ]=\mathcal O\). In this survey, we give an overview of recent results on estimates for the number of \(\alpha\) up to equivalence. Cited in 1 ReviewCited in 5 Documents MSC: 11R04 Algebraic numbers; rings of algebraic integers 11D57 Multiplicative and norm form equations 11-02 Research exposition (monographs, survey articles) pertaining to number theory Keywords:monogenic orders Citations:Zbl 0354.10041 PDFBibTeX XMLCite \textit{J.-H. Evertse}, Publ. Math. Debr. 79, No. 3--4, 411--422 (2011; Zbl 1249.11102) Full Text: DOI