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Diophantine equations in cyclotomic fields.

open access: yesJournal für die reine und angewandte Mathematik (Crelles Journal), 1974
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MONOGENEITY IN CYCLOTOMIC FIELDS

International Journal of Number Theory, 2010
A number field is said to be monogenic if its ring of integers is a simple ring extension ℤ[α] of ℤ. It is a classical and usually difficult problem to determine whether a given number field is monogenic and, if it is, to find all numbers α that generate a power integral basis {1, α, α2, …, αk} for the ring.
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