By Mike Prest

It really is attainable to affiliate a topological area to the class of modules over any ring. This area, the Ziegler spectrum, relies at the indecomposable pure-injective modules. even though the Ziegler spectrum arose in the version thought of modules and performs a critical function in that topic, this publication concentrates in particular on its algebraic points and makes use of. The crucial target is to appreciate modules and the kinds they shape via linked buildings and dimensions, which replicate the complexity of those, and comparable, different types. The buildings and dimensions thought of come up relatively in the course of the program of model-theoretic and functor-category rules and strategies. Purity and linked notions are important, localisation is an ever-present subject and diverse varieties of spectrum play establishing roles. This e-book offers a unified, coherent account of fabric that's usually awarded from very diversified viewpoints and clarifies the relationships among those a variety of ways.