About This Book This book is meant to be used by beginning graduate
students. It covers basic material needed by any student of algebra, and
is essential to those specializing in ring theory, homological algebra,
representation theory and K-theory, among others. It will also be of
interest to students of algebraic topology, functional analysis,
differential geometry and number theory. Our approach is more
homological than ring-theoretic, as this leads the to many important
areas of mathematics. This ap- student more quickly proach is also, we
believe, cleaner and easier to understand. However, the more classical,
ring-theoretic approach, as well as modern extensions, are also
presented via several exercises and sections in Chapter Five. We have
tried not to leave any gaps on the paths to proving the main theorem- at
most we ask the reader to fill in details for some of the sideline
results; indeed this can be a fruitful way of solidifying one's
understanding.