This book describes a constructive approach to the inverse Galois problem: Given a finite group G and a field K, determine whether there exists a Galois extension of K whose Galois group is… Expand

To mot ivate the following results let us recall some definitions and results with relation to the m o m e n t problem. Let (S, + ) be an abelian semigroup with neutral element 0. A real-valued… Expand

Introduction, ultraproducts, definitions and examples elementary equivalence - axiomatizable and finitely axiomatizable classes - examples and results in field theory elementary definability -… Expand

Proof. Since an ideal a in R is uniquely determined by its local components dm and the formation of sums and intersections of ideals is preserved by extension from R to Rm it suffices to prove that a… Expand

Abstract For an algebraic number field K we study the quadratic extensions of K which can be embedded in a cyclic extension of K of degree 2 n for all natural numbers n, as well as the quadratic… Expand