Advances in Algebra and Model Theory: Selected surveys presented at conferences in Essen 1994 and Dresden 1995 (Algebra, Logic and Applications)

Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. Cover Half Title Series Page Title Page Copyright Page Contents Preface Acknowledgements Conference Lecturers Elimination over skew fields Elementary questions in Galois theory On orderings of higher level Groups with Hrushovski-geometries Finite covers of .[(sub(0)]-categorical structures Orbits of soluble infinite permutation groups Aspects of cofinitary permutation groups Cofinalities of infinite permutation groups Joint embeddings of infinite permutation groups Varieties and universal words for automorphism groups of orders Semilinearly ordered groups An invitation to Changs MV algebras Applications of .-filtered Boolean algebras The model theory of abelian p-groups Non-existence of universals for classes like reduced torsion free abelian groups under embeddings which are not necessarily pure Infinite rank Butler groups Endomorphism rings of torsion-free abelian groups of finite rank A class of potential counter-examples to the pure semisimplicity conjecture Generic modules over tubular algebras A construction of endofinite modules Finitely generated modules over pullback rings and algebras The Boboli garden of uniserial modules Divisible uniserial modules over valuation domains Purity in model theory Modules over non-perfect rings some recent concepts and results suggested by abelian group theory Index Over a commutative field there is a process known as the elimination of quantifiers, which is very useful.