Displaying similar documents to “Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields”

Hasse’s problem for monogenic fields

Toru Nakahara (2009)

Annales mathématiques Blaise Pascal

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In this article we shall give a survey of Hasse’s problem for integral power bases of algebraic number fields during the last half of century. Specifically, we developed this problem for the abelian number fields and we shall show several substantial examples for our main theorem [] [], which will indicate the actual method to generalize for the forthcoming theme on Hasse’s problem [].

A generalization of Voronoï’s Theorem to algebraic lattices

Kenji Okuda, Syouji Yano (2010)

Journal de Théorie des Nombres de Bordeaux

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Let K be an algebraic number field and 𝒪 K the ring of integers of K . In this paper, we prove an analogue of Voronoï’s theorem for 𝒪 K -lattices and the finiteness of the number of similar isometry classes of perfect 𝒪 K -lattices.