Synopses & Reviews
This book provides a sampling of recent advances in ordered algebraic structures, with emphasis on developments in areas where general topology, category theory and model theory play a prominent role. The discourse in ordered algebra has been significantly affected by other disciplines, and this volume is representative of that trend. Audience: This volume will appeal to mathematicians with a wide range of interests, particularly in topology, and the topology of rings of functions.
Synopsis
The conference on Ordered Algebraic Structures held in Curat;ao, from the 26th of June through the 30th of June, 1995, at the Avila Beach Hotel, marked the eighth year of ac tivities by the Caribbean Mathematics Foundation (abbr. CMF), which was the principal sponsor of this conference. CMF was inaugurated in 1988 with a conference on Ordered Algebraic Structures. During the years between these two conferences the field has changed sufficiently, both from my point of view and, I believe, that of my co-organizer, W. Charles Holland, to make one wonder about the label "Ordered Algebraic Structures" itself. We recognized this from the start, and right away this conference carried a subtitle, or, if one prefers, an agenda: we concentrated on the one hand, on traditional themes in the theory of ordered groups, including model-theoretic aspects, and, on the other hand, on matters in which topology (more precisely C(X)-style topology) and category theory would play a prominent role. Plainly, ordered algebra has many faces, and it is becoming increas ingly difficult to organize an intimate conference, such as the ones encouraged in the series sponsored by CMF, in this area on a broad set of themes. These proceedings reflect, accurately we think, the spirit of the conferees, but it is not a faithful record of the papers presented at the conference."
Table of Contents
Preface. A Survey of f-Rings and Some of Their Generalizations; M. Henriksen. Reflections on the Global Dimensions of Rings of Continuous Functions; R.T. Finn. Continuous Ultraproducts; N.L. Alling. Actions on Archimedean Lattice-Ordered Groups with Strong Unit; R.N. Ball, J.N. Hagler. Pointfree Topology and the Spectra of f-Rings; B. Banaschewski. Commutative Singular f-Rings; R.T. Finn, et al. Torsion Classes of Lattice-Ordered Groups with Invariant Radicals; P.F. Conrad, M.R. Darnel. The Automorphism Groups of Hahn Groups; M. Droste, R. Göbel. The Laterally sigma-Complete Reflection of an Archimedean Lattice-Ordered Group; A.W. Hager, J. Martinez. Ax-Kochen-Ershov Principles for Valued and Ordered Vector Spaces; F. Viktor, S. Kuhlmann. Quasi-Normal f-Rings; S. Larson. Rings of Continuous Functions as Real Closed Rings; N. Schwartz. On Universal Words for Automorphism Groups of Linear Orders; L.V. Welch, S.A. Adeleke.