Steps in commutative algebra

This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of nonexperts, mathematicians whose speciality is not ring theory, will find Ring Theory ideally suited to their needs....They, as well as students, will be well served by the many examples of rings and the glossary of major results."**--NOTICES OF THE AMS Commutative rings and subrings -- Ideals -- Prime ideals and maximal ideals -- Primary decomposition -- Rings of fractions -- Modules -- Chain conditions on modules -- Commutative noetherian rings -- More module theory -- Modules over principal ideal domains -- Canonical forms for square matrices -- Some applications to field theory -- Integral dependence on subrings -- Affine algebras over fields -- Dimension theory -- Regular sequences and grade -- Cohen-macalay rings