© 2017

Formal Matrices


Part of the Algebra and Applications book series (AA, volume 23)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Piotr Krylov, Askar Tuganbaev
    Pages 1-2
  3. Piotr Krylov, Askar Tuganbaev
    Pages 3-30
  4. Piotr Krylov, Askar Tuganbaev
    Pages 31-88
  5. Piotr Krylov, Askar Tuganbaev
    Pages 89-128
  6. Piotr Krylov, Askar Tuganbaev
    Pages 129-150
  7. Back Matter
    Pages 151-156

About this book


This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory.

While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings.

Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.


formal matrix generalized matrix Morita context Grothendieck group Whitehead group injective module flat module projective module determinant ring theory K-theory

Authors and affiliations

  1. 1.Tomsk State University TomskRussia
  2. 2.Moscow Power Engineering Institute MoscowRussia

Bibliographic information


“This book is an attempt to give a rather comprehensive treatment of formal matrix rings. … I strongly recommend this book; it should definitely be in every serious university's library.” (Leon Van Wyk, Mathematical Reviews, November, 2017)

“The book is written in a friendly style. The presentation is clear and many good examples are given to illustrate the main concepts and results. The book is useful to researchers in ring theory and linear algebra. It is also suitable for graduate students.” (Sorin Dascalescu, zbMATH 1367.16001, 2017)