This book is an introduction to the theory of rings and modules
that goes beyond what one normally obtains in a graduate course in
abstract algebra. The theme of the text is the interplay between
rings and modules. At times rings are investigated by considering
given sets of conditions on the modules they admit and at other
times rings of a certain type are considered to see what structure
is forced on their modules. Standard topics in ring and module
theory such as chain conditions on rings and modules, injective and
projective modules and semisimple rings are included as well as
subjects like category theory and homological algebra. The text
also contains presentations on topics such as flat modules and
coherent rings, injective envelopes, projective covers and perfect
rings, reflexive modules and quasi-Frobenius rings, and graded
rings and modules. The book is a self-contained volume written in a
very systematic style: allproofs are clear and easy for the reader
to understand and allarguments are based on materials contained in
the book. A problem sets follow each section. It is assumed that
the reader is familiar with concepts such as Zorn's lemma,
commutative diagrams and ordinal and cardinal numbers. It is also
assumed that the reader has a basic knowledge of rings and their
homomorphisms. The text is suitable for graduate and PhD students
who have chosen ring theory for their research subject.
General
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