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

✍ Scribed by M Droste (editor), R. Gobel (editor)

• Publisher: CRC Press
• Year: 1998
• Tongue: English
• Leaves: 512
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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 Chang’s 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