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In this book, ring-theoretical properties of skew Laurent series
rings A((x; )) over a ring A, where A is an associative ring with
non-zero identity element are described. In addition, we consider
Laurent rings and Malcev-Neumann rings, which are proper extensions
of skew Laurent series rings.
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.
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.
This book offers a comprehensive account of not necessarily
commutative arithmetical rings, examining structural and
homological properties of modules over arithmetical rings and
summarising the interplay between arithmetical rings and other
rings, whereas modules with extension properties of submodule
endomorphisms are also studied in detail. Graduate students and
researchers in ring and module theory will find this book
particularly valuable.
The theory of invariance of modules under automorphisms of their
envelopes and covers has opened up a whole new direction in the
study of module theory. It offers a new perspective on
generalizations of injective, pure-injective and flat-cotorsion
modules beyond relaxing conditions on liftings of homomorphisms.
This has set off a flurry of work in the area, with hundreds of
papers using the theory appearing in the last decade. This book
gives the first unified treatment of the topic. The authors are
real experts in the area, having played a major part in the
breakthrough of this new theory and its subsequent applications.
The first chapter introduces the basics of ring and module theory
needed for the following sections, making it self-contained and
suitable for graduate students. The authors go on to develop and
explain their tools, enabling researchers to employ them, extend
and simplify known results in the literature and to solve
longstanding problems in module theory, many of which are discussed
at the end of the book.
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