On a Problem of Hasse for Certain Imaginary Abelian Fields Original Research Article

Let K be the composite field of an imaginary quadratic field Q(ω) of conductor d and a real abelian field L of conductor f distinct from the rationals Q, where (d,f)=1. Let ZK be the ring of integers in K. Then concerning to Hasseʹs problem we construct new families of infinitely many fields K with the non-monogenic phenomena (1), (2) which supplement (J. Number Theory23 (1986), 347–353; Publ. Math. Fac. Sci Besançon, Theor. Nombres (1984) 25pp) and with monogenic (3).