Noncommutative Localization in Algebra and Topology (London Mathematical Society Lecture Note Series Book 330) 1st Edition by Andrew Ranicki (PDF)

Description

Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐These xiii+313 pages of conference proceedings are bound and printed very nicely indeed, with a short but valuable index.I bought this volume 3 years ago (in early 2014) in the hope of finding some elementary constructions for noncommutative ordered rings, maybe using Laurent series of some kind. In fact, I believe there are examples of such constructions in Sections 17 and 18 of Lam’s textbook, ”

⭐”, which I do not yet possess. But unfortunately, I have not found any suitable examples in these conference papers, which are far too research-oriented to provide such elementary material, although I did find some Laurent series constructions on pages 83, 93, 113, 116, 149, and some Malcev-Neumann constructions on pages 9, 45, 53. Otherwise, I haven’t yet been able to associate these conference proceedings with any kind of mathematics that I have ever done before. Maybe an algebraist could write a review of this volume here. This book makes me realise that I will never be an algebraist!

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