Slenderness: Volume 1, Abelian Categories

A leading expert presents a unified concept of slenderness in Abelian categories, with numerous open problems and exercises.

Radoslav Dimitric (Author)

9781108474429, Cambridge University Press

Hardback, published 6 December 2018

330 pages, 355 exercises
23.6 x 15.7 x 2.2 cm, 0.57 kg

'At the end of every chapter some exercises, problems and notes are gathered which could be very useful for understanding the theory and for future research on this subject.' George Ciprian Modoi, MathSciNet

Slenderness is a concept relevant to the fields of algebra, set theory, and topology. This first book on the subject is systematically presented and largely self-contained, making it ideal for researchers and graduate students. The appendix gives an introduction to the necessary set theory, in particular to the (non-)measurable cardinals, to help the reader make smooth progress through the text. A detailed index shows the numerous connections among the topics treated. Every chapter has a historical section to show the original sources for results and the subsequent development of ideas, and is rounded off with numerous exercises. More than 100 open problems and projects are presented, ready to inspire the keen graduate student or researcher. Many of the results are appearing in print for the first time, and many of the older results are presented in a new light.

Introduction
1. Topological rings and modules and their completions
2. Inverse limits
3. The idea of slenderness
4. Objects of type ? / coprod
5. Concrete examples. Slender rings
6. More examples of slender objects
Appendix. Ordered sets and measurable cardinals
References
Notation index
Name Index
Subject index.

Subject Areas: Algebraic topology [PBPD], Algebra [PBF], Set theory [PBCH], Mathematical logic [PBCD]