Publisher's Synopsis
One important theme in algebra and functional analysis has been the representation of various rings or algebras using continuous functions defined on their spectra or Boolean spectra.;These notes show that many naturally described rings can be represented using specified continuous functions from dense open subsets of their Boolean spectra into an indecomposable ring and the book also determines up to elementary equivalence all rings which have such a representation.;In order to accomplish these, the work casts the entire problem in the framework of ring localizations and model completions. This framework is developed in substantial generality and illustrated with examples. Later this framework is applied to accomplish these objectives by obtaining detailed information about the topology of the Pierce sheaf of suitable rings. Several examples are given of rings that can not be represented in this fashion.;The Pierce sheaf has been widely used as a tool in ring theory. However applications of this tool normally exploit the algebraic structure of the stalks and the topology of the base space. These notes deal with the topology of the sheaf itself and use the results obtained to represent suitable rings in the manner described in the text.
