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.
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