David M. Arnold

A recurring theme in a traditional introductory graduate algebra course is the existence and consequences of relationships between different algebraic structures. This is also the theme of this book, an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals. His research interests are in abelian group theory and related topics, such as representations of partially ordered sets and modules over discrete valuation rings, subrings of algebraic number fields, and pullback rings. He received his Ph. D. from the University of Illinois, Urbana and was a member of the faculty at New Mexico State University for many years.

This informative volume contains the proceedings of the international conference on abelian groups and modules held recently in Colorado Springs - presenting the latest developments in abelian groups that have facilitated cross-fertilization of new techniques from diverse areas such as the representation theory of posets, model theory, set theory, and module theory. Providing an overview of current research directions, Abelian Groups and Modules offers original contributions from over 33 conference participants on topics such as finite rank Butler groups ... almost completely decomposable groups ... Butler groups of infinite rank ... mixed groups ... torsion-free abelian groups ... modules over chain rings ... set/model theoretical applications ... category arguments and descriptive set theory ... applications to algebra ... and more. Including a number of open questions and problems, Abelian Groups and Modules is an outstanding reference for algebraists; group, module, and number theorists; and graduate mathematics students.