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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