The four hundred problems in the first edition of this book were largely
based on the original collection of exercises in my Springer Graduate Text
A First Course in Noncommutative Rings, ca. 1991. A second edition of this
ring theory text has since come out in 2001. Among the special features of
this edition was the inclusion of a large number of newly designed exercises,
many of which have not appeared in other books before.
It has been my intention to make the solutions to these new exercises
available. Since Exercises in Classical Ring Theory has also gone out of
print recently, this seemed a propitious time to issue a new edition of our
Problem Book. In this second edition, typographical errors were corrected,
various improvements on problem solutions were made, and the Comments
on many individual problems have been expanded and updated. All in all,
we have added eighty-five exercises to the first edition, some of which are
quite challenging. In particular, all exercises in the second edition of First
Course are solved here, with essentially the same reference numbers. As
before, we envisage this book to be useful in at least three ways: (1) as
a companion to First Course (second edition), (2) as a source book for
self-study in problem-solving, and (3) as a convenient reference for much
of the folklore in classical ring theory that is not easily available elsewhere.