Decomposition of primes in non-maximal orders
Decomposition of primes in number fields defined by trinomials
In this paper we deal with the problem of finding the prime-ideal decomposition of a prime integer in a number field defined by an irreducible trinomial of the type , in terms of and . We also compute effectively the discriminant of .
Die irreduziblen Zahlen des Bereichs Z [...-5].
Die Klassenzahl der Teilkörper abelscher Erweiterungen imaginär-quadratischer Zahlkörper. II.
Die Klassenzahl der Teilkörper abelscher Erweiterungen imaginär-quadratischer Zahlkörper. I.
Die Struktur der Einheitengruppe für eine Klasse metazyklischer Erweiterungen algebraischer Zahlkörper.
Differences in sets of lengths of Krull monoids with finite class group
Let be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary -groups have the same system of sets of lengths if and only if they are isomorphic.
Different groups of circular units of a compositum of real quadratic fields
There are many different definitions of the group of circular units of a real abelian field. The aim of this paper is to study their relations in the special case of a compositum k of real quadratic fields such that -1 is not a square in the genus field K of k in the narrow sense. The reason why fields of this type are considered is as follows. In such a field it is possible to define a group C of units (slightly bigger than Sinnott's group of circular units) such that the Galois...
Diophantine equations and identities.
Diophantine equations in cyclotomic fields.
Distributions on Toroidal Groups.
Divisibility of class numbers of real cyclic extensions of degree 4 over Q.