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This is the first monograph devoted to clean ring and matrix
theory. It aims to study a theory of expressing an element in a
ring as the sum of some special ones, such as idempotents, units,
nilpotents, tripotents, involutions, etc. A matrix over such rings
is thereby expressed as the sum of some special matrices. Also
another topics on the behaviors of topological properties and
*-properties of such rings are investigated.The book is based on
the results of various published papers, particularly, by the
authors'. It is accessible for students familiar with general
abstract algebra, while the topics are interesting for researchers
in the field of ring, matrix and operator theory.
This monograph is concerned with exchange rings in various
conditions related to stable range. Diagonal reduction of regular
matrices and cleanness of square matrices are also discussed.
Readers will come across various topics: cancellation of modules,
comparability of modules, cleanness, monoid theory, matrix theory,
K-theory, topology, amongst others. This is a first-ever book that
contains many of these topics considered under stable range
conditions. It will be of great interest to researchers and
graduate students involved in ring and module theories.
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