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The purpose of this book is to generalize to the
torsion-theoretic setting various concepts and
results from the theory of rings and modules. In
particular we work in the areas of chain conditions
on modules, injectivity and CS (extending) modules.
At the outset we acquaint the reader with the main
ideas used in torsion theory. We then obtain results
that fall into three more or less interrelated areas.
In the first area we introduce a torsion-theoretic
analogue of Max modules and generalize an important
characterization of Noetherian rings by Shock. The
second area deals with various flavors of relative
injectivity. We generalize well-known results by
Fuchs, Azumaya, Faith, Albu and Nastasescu and
Cailleau. In the third area we introduce a couple of
new concepts with the aim of bringing to the
torsion-theoretic setting the concept of a CS or
extending module. Our motivation is to provide a
torsion-theoretic analogue of a celebrated result by
Okado.
This book should appeal to researchers in the theory
of rings and modules with particular emphasis on
torsion theory.
torsion-theoretic setting various concepts and
results from the theory of rings and modules. In
particular we work in the areas of chain conditions
on modules, injectivity and CS (extending) modules.
At the outset we acquaint the reader with the main
ideas used in torsion theory. We then obtain results
that fall into three more or less interrelated areas.
In the first area we introduce a torsion-theoretic
analogue of Max modules and generalize an important
characterization of Noetherian rings by Shock. The
second area deals with various flavors of relative
injectivity. We generalize well-known results by
Fuchs, Azumaya, Faith, Albu and Nastasescu and
Cailleau. In the third area we introduce a couple of
new concepts with the aim of bringing to the
torsion-theoretic setting the concept of a CS or
extending module. Our motivation is to provide a
torsion-theoretic analogue of a celebrated result by
Okado.
This book should appeal to researchers in the theory
of rings and modules with particular emphasis on
torsion theory.