Classes de steinitz et extensions quaternioniennes
Author
Massy, Richard
Sodaïgui, Bouchaib
Abstract
Let k be a number field. We prove that the set of Steinitz clases of quadratic extensions K/ k which can be embedded in quaternionic extensions of degree 8, tamely or wildly ramified over k, is the full class group Cl(k) of k. Moreover, we provide explicit formulas to construct these quaternionic extensions.