Ordered Algebraic Structures: Proceedings of the Gainesville Conference Sponsored by the University of Florida 28th February ― 3rd March, 2001 (Developments in Mathematics (7))

From the 28th of February through the 3rd of March, 2001, the Department of Math­ ematics of the University of Florida hosted a conference on the many aspects of the field of Ordered Algebraic Structures. Officially, the title was "Conference on Lattice­ Ordered Groups and I-Rings", but its subject matter evolved beyond the limitations one might associate with such a label. This volume is officially the proceedings of that conference, although, likewise, it is more accurate to view it as a complement to that event. The conference was the fourth in wh at has turned into aseries of similar conferences, on Ordered Algebraic Structures, held in consecutive years. The first, held at the University of Florida in Spring, 1998, was a modest and informal affair. The fifth is in the final planning stages at this writing, for March 7-9, 2002, at Vanderbilt University. And although these events remain modest and reasonably informal, their scope has broadened, as they have succeeded in attracting mathematicians from other, related fields, as weIl as from more distant lands. Front Matter....Pages i-xi Front Matter....Pages 1-1 The Bornological Tensor Product of two Riesz Spaces....Pages 3-9 Old and New Unsolved Problems in Lattice-Ordered Rings that need not be f -Rings....Pages 11-17 A Survey of Residuated Lattices....Pages 19-56 MV-Algebras and Abelian l -Groups: a Fruitful Interaction....Pages 57-88 Hull Classses of Archimedean Lattice-Ordered Groups with Unit: A Survey....Pages 89-121 Surveying Lattice-Ordered Fields....Pages 123-153 Front Matter....Pages 155-155 Stone’s Real Gelfand Duality in Pointfree Topology....Pages 157-177 The Range of Lattice Homomorphisms on f -Algebras....Pages 179-188 The Bornological Tensor Product of two Riesz spaces: Proof and Background Material....Pages 189-203 Non-distributive Cancellative Residuated Lattices....Pages 205-212 Reconstructing C ( G ) from a Plenary Subset....Pages 213-230 The Undecidability of the Word Problem for Distributive Residuated Lattices....Pages 231-243 Least Integer Closed Groups....Pages 245-260 Structure Spaces of Maximal l -Ideals of Lattice-Ordered Rings....Pages 261-274 Polar Functions, I: The Summand-Inducing Hull of an Archimedean l -Group with Unit....Pages 275-299 A Priestley-type Method for Generating Free l -Groups....Pages 301-312 On the Flatness of the Epimorphic Hull of a Ring of Continuous Functions....Pages 313-321 Back Matter....Pages 323-323 From the 28th of February through the 3rd of March, 2001, the Department of MathƯ ematics of the University of Florida hosted a conference on the many aspects of the field of Ordered Algebraic Structures. Officially, the title was "Conference on LatticeƯ Ordered Groups and I-Rings", but its subject matter evolved beyond the limitations one might associate with such a label. This volume is officially the proceedings of that conference, although, likewise, it is more accurate to view it as a complement to that event. The conference was the fourth in wh at has turned into aseries of similar conferences, on Ordered Algebraic Structures, held in consecutive years. The first, held at the University of Florida in Spring, 1998, was a modest and informal affair. The fifth is in the final planning stages at this writing, for March 7-9, 2002, at Vanderbilt University. And although these events remain modest and reasonably informal, their scope has broadened, as they have succeeded in attracting mathematicians from other, related fields, as weIl as from more distant lands This publication surveys some of the disciplines within ordered algebraic structures and also contains chapters highlighting a broad spectrum of research interests. In all, this book represents a reasonably accurate cross-section of the state of the art in ordered algebraic structures.