GTM211-Algebra

FOREWORDThe present book is meant as a basic text for a one-year course in algebra,
at the graduate level .
A perspective on algebra
As I see it, the graduate course in algebra must primarily prepare students
to handle the algebra which they will meet in all of mathematics: topology,
partial differential equations, differential geometry, algebraic geometry, analysis ,
and representation theory, not to speak of algebra itself and algebraic number
theory with all its ramifications . Hence I have inserted throughout references to
papers and books which have appeared during the last decades , to indicate some
of the directions in which the algebraic foundations provided by this book are
used ; I have accompanied these references with some motivating comments, to
explain how the topics of the present book fit into the mathematics that is to
come subsequently in various fields; and I have also mentioned some unsolved
problems of mathematics in algebra and number theory . The abc conjecture is
perhaps the most spectacular of these.